Continuum Actuator Based Soft Quadruped Robot

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IN

DEGREE PROJECT MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

,

STOCKHOLM SWEDEN 2020

Continuum Actuator Based

Soft Quadruped Robot

SESHAGOPALAN THORAPALLI

MURALIDHARAN

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Abstract

Master of Science ThesisMMK TRITA-ITM-EX 2020:587

Continuum Actuator Based Soft Quadruped Robot

Seshagopalan Thorapalli Muralidharan Ruihao Zhu Approved 2020-11-18 Examiner Lei Feng Supervisor Qinglei Ji Commissioner Lei Feng Contact person Lei Feng

Quadruped robots can traverse a multitude of terrains with greater ease when compared to wheeled robots. Traditional rigid quadruped robots possess severe limitations as they lack structural compliance. Most of the existing soft quadruped robots are tethered and are actuated using pneumatics, which is a low grade energy source and lacks viability for long endurance robots. The work in this thesis proposes the development of a continuum actuator driven quadruped robot which can provide compliance while being un-tethered and electro-mechanically driven.

In this work, continuum actuators are developed using mostly 3D printed parts. Additionally, the closed loop control of continuum actuators for walking is developed. Linear Quadratic Regulator (LQR) and pole placement based methods for controller synthesis were evaluated and LQR was determined to be better when minimizing the actuator effort and deviation from set-point.

These continuum actuators are composed together to form a quadruped. Gait analyses on the quadruped were conducted and legs of the quadruped were able to trace the gaits for walking and galloping.

KeywordsSoft robots, continuum actuators, closed loop control, quadruped

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Sammanfattning

Examensarbete MMK TRITA-ITM-EX 2020:587

Fyrbent Mjuk Robot baserad på Kontinuerligt Deformerbara Ställdon

Seshagopalan Thorapalli Muralidharan Ruihao Zhu Godkänt 2020-11-18 Examinator Lei Feng Handledare Qinglei Ji Uppdragsgivare Lei Feng Kontaktperson Lei Feng

Fyrfotarobotar kan lättare korsa en mängd olika terränger jämfört med hjulrobotar. Traditionella styva fyrfotarobotar har kraftiga begränsningar d˚a de saknar strukturell följsamhet. De flesta befintliga mjuka fyrbenta robo-tar är kopplade till en eller flera kablar och drivs av pneumatik, vilket är en l˚agkvalitativ energikälla och lämpar sig inte för robotar med l˚ang uth˚allighet. Arbetet i denna avhandling föresl˚ar utvecklingen av en continuum ställdons-driven fyrfotarobot, som ger följsamhet samtidigt som den är fr˚ankopplad och elektromekaniskt driven.

I detta arbete framställs continuum ställdon med mestadels 3D-printade delar. Dessutom utvecklas dessa ställdons slutna kontrolloop för g˚ang.

Linj¨ark-vadratisk regulator (LQR) och metoder baserade p˚a polplacering utv¨arderades

för styrsyntes, och det fastställdes att LQR presterade bättre när man min-imerar ställdonets ansträngning samt avvikelse fr˚an referensvärde.

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Acknowledgements

We would first like to thank our supervisor Qinglei Ji who was there for us at every step of the way, providing us with unflinching and unwavering support. Your valuable suggestions, ideas, helping us formulate our research question and providing us with all resources to undertake this thesis.

We would like to thank Professor Lei Feng, for his support, ideas, and feedback towards making this a successful thesis project.

Additionally, we would like to thank our lab mates Shuo Fu, Mo Chen and Sudanshu Kuthe for keeping us company and taking part in some of our discussions.

Finally we would like to thank our parents, friends and fellow classmates who have provided us with immense inspiration and support.

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List of Figures

1.1 Spring Based Continuum Actuator . . . 3

2.1 A typical cable driven continuum actuator . . . 12

2.2 Actuator Design Parameters . . . 12

2.3 Workspace of the soft actuator . . . 14

2.4 Screw-less assembly of the motor and its associated components . 14 2.5 Rendered CAD model of the actuator . . . 16

2.6 Comparison of the infill on the actuators . . . 17

2.7 PCB and Micro-controller for Controlling a Continuum Actuator . 20 2.8 The GUI developed for calibration and testing . . . 21

2.9 Rendered exploded view of the continuum actuator and its sup-porting accessories . . . 22

2.10 A plot of the Motor Positions and Potentiometer Position . . . . 25

2.11 Step response of the motor . . . 26

2.12 Structure of system for model estimation data collection . . . 27

2.13 Actuator Motor Performance . . . 28

2.14 The data used to fit the model . . . 29

2.15 Input data applied to the estimated model . . . 30

2.16 General control structure of a continuum actuator . . . 31

2.17 Plot of RMS error and Actuator Effort . . . 33

2.18 Simulated LQR controller . . . 34

2.19 Hardware implemented LQR controller . . . 35

2.20 Pole Placement RMS Error vs Actuator Effort . . . 36

2.21 Simulated Closed Loop Pole Placement System . . . 37

3.1 Overall view of the soft quadruped platform . . . 40

3.2 A fully assembled and mounted quadruped . . . 40

3.3 Electronics hardware Overview of the Quadruped . . . 42

3.4 Oscillator based generation of walking sequence . . . 43

3.5 Walking gait . . . 44

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A1 Electronics hardware Overview of the Quadruped . . . 59

A2 The Simulink external mode control dashboard for the Quadruped 61 A3 BendRot/ABC block expanded . . . 62

A4 Receive block expanded . . . 63

A5 Send data block expanded . . . 64

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List of Tables

1.1 Non-extensive comparision of work in quadruped robots . . . 4

2.1 Model order vs accuracy . . . 29

3.1 Gait sequence phase shifts . . . 43

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Acronyms

3D Three Dimension.

ADC Analog to Digital Converter.

ARM Advanced RISC Machines.

CAD Computer Aided Design.

DARPA Defense Advanced Research Projects Agency.

DMA Direct Memory Access.

DOF Degees of Freedom.

ETH Swiss Federal Institute of Technology.

FDM Fused Deposition Modelling.

GPIO General Purpose Input Output.

GUI Graphical User Interface.

IC Integrated Circuit.

IIT Italian Institute of Technology.

LP Low Pass.

LQR Linear Quadratic Regulator.

MIMO Multiple Input Multiple Output.

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PCB Printed Circuit Board.

PWM Pulse Width Modulation.

R-C Resistor Capacitor.

RC Radio Control.

STM STMicroelectronics.

TI Texas Instruments.

TPU Thermoplastic Polyurethane.

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Chapter 1 Introduction

1.1 Overview of Quadruped Robots

Quadruped robots are four legged robots which generally mimic animal characteristics [1][2] such as those of cats, dogs and cheetahs. Theoretically, these can be superior to wheeled robots in their ability to traverse uneven terrain [2][3]. This ability is important considering that most of the earth is unpaved and uneven. Designing and developing bio-mimicking robots has received a push following the DARPA robotics challenge [4]. Quadrupedal robots are typically designed to handle dynamic outdoor environments in the absence of human interaction [3]. Over the last few years a substantial amount of work has been devoted into the research of quadrupedal robots, notable ones are Boston Dynamics Big Dog [5], IIT’s HyQ2Max [3], MIT’s Cheetah [6] and ETH Zurich’s ANYmal [7]. However, quadrupeds fail to achieve comparative results with legged animals due to their low endurance, poor physical skills, lack of cognition and inability to consistently traverse difficult terrain [8] [9].

1.2 Overview of Soft Robots

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CHAPTER 1. INTRODUCTION

constructed using flexible materials with a young’s modulus in the range of 104

to 109

Pa [11]. The soft structures of these robots are traditionally actuated using pneumatic, thermal, magnetic or photo-sensitive methods. Most current soft robots are pneumatically actuated, due to which additional compliance is obtained [10][12][15]. Traditionally, study in soft robots has been limited to research by material scientists, however, with the advent of 3D printing, 3D printable sensors and miniaturization of sensors[16], the ease of manufacturing soft robots has increased. This paves the way to examine various methods to control these robots [14][15].

Complete proprioceptive position estimation of soft robots has been par-ticularly challenging owing to fact that soft robots deform along the region of the applied actuation forces (pneumatic, thermal etc) [17]. Additionally, esti-mating the mode shape of the bending given an external contact force can be challenging as the region of deformation is generally local with global implica-tions, given a point load. This presents issues in control of soft robots as the 3D location and magnitudes of the point loads need to be estimated in order to estimate the mode shape with reasonable accuracy. Additionally, increased actuation forces can generally only be applied to actuators as a whole, which limits the extent of control. Substantial strides have been made in computer vision driven exoceptive measurement and sensing of mode shapes and posi-tions of soft robotic actuators [14]. However, the very nature of exoceptive sensors greatly reduces the application space for such soft robots. Therefore, truly independent soft robots needs to implement a full set of proprioceptive sensors with highly quantized and discretized actuation in order to generate distinct actuator efforts to overcome applied loads [17].

1.3 Overview of Continuum Actuators

Continuum actuators are actuators which can deform along their whole length. An example of this are elephant trunk like actuators, which are semi-soft robotic actuators which possess the ability to deform over the length of the actuator [18]. This type actuator also finds applications in minimally invasive surgery [19]. An implementation of this is an actuator which uses 3 individual wires in order to execute 3 DOF motion [20](as shown in Figure 1.1). The application of a tensile force on actuation wires results in bending motion [21]. The core of the actuator is typically a spring (linear and torsional) which applies a restoring force when loaded. This ensures the restoring force applied by the actuator is limited by the mechanical stiffness of the spring [22]. These actuators traditionally consisted of rigid plates and springs actuated

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1.4. PROPOSED SOFT CONTINUUM QUADRUPED

with wires. These are generally not regarded as true ”soft robots” as their main components are largely rigid.

Figure 1.1: Spring Based Continuum Actuator (regenerated from [23] IEEE ©[2007])

1.4 Proposed Soft Continuum Quadruped

Traditionally quadrupedal robots consist of rigid links. However, rigid links exhibit poor compliance. Quadrupeds with greater passive structural compliance can crawl into smaller spaces and traverse uneven environments [9]. Since most soft robotic actuators are omni-directional, the final motion of the robot can also be planar omni-directional, this overcomes the planar non-holonomic constraints of traditional quadrupedal robots. The soft limbs ensure that the contact forces between the robot and other objects are kept to a minimum, due to which damage to both the robot and surroundings is minimum in case of large contact forces. Although contact forces may act on a single point on the actuator, the force is distributed as the whole actuator deforms [24]. Therefore, a soft quadrupedal may be superior to a rigid quadruped in overcoming distributed and point loads while exhibiting planar omni-directionality.

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in order to actuate. Gases are low grade energy sources as their energy per unit volume (at constant pressure) is lower than that of liquids (hydraulic). [25]. As a consequence, soft robots generally require tethers which either supply them with air or electricity to power on-board compressors. An un-tethered soft robot, could implement electro-mechanical actuation as both mechanical and electric energy are high grade energy sources. Direct electrical actua-tion such as Electric Activated Polymer(EAP) have shown promise but are generally slower in their speed of operation compared to electro-mechanical actuation [26].

Continuum actuators are suitable for quadrupeds as quadrupeds require

at least 2 Degees of Freedom (DOF) in each leg [27] for walking.

Con-tinuum actuators can be pneumatic or electro-mechanically driven [12][26]. Non-continuum actuator based pneumatic soft quadrupedal robots have al-ready been developed and tested [12] and a non-extensibe comparision of some quadrupeds along with the proposed quadruped has been provided in table 1.1. However, these robots are tethered. It is proposed that a continuum actuator (as shown in Figure 1.1) consisting of 3 wires can create bending and longitudinal movement. In the proposed robot, the wires would be actuated using electric motors. Rotary positional encoders may be used to monitor the wire position. Current sensors on the motor can provide an estimate of the actuator effort. Actuator effort and positional data can be used to estimate the bending state of the actuator. Further, a micro-controller will be perform-ing closed loop control of the system and achieve the required bendperform-ing state of the actuator.

Quadruped Robot Source RobotType Year Actuation

Type

Thether

Boston Dynamics

Big Dog

[5] Rigid 2005 Pneumatic Untethered

Harvard Multigait Soft Robot

[28] Soft 2011 Hydraulic Tethered

Harvard Resilient

Quadruped Robot

[9] Soft 2014 Pneumatic Untethered

Dielectric Crawler [29] Soft 2017 Electric Untethered

MIT Cheetah [8] Rigid 2018 Electric Untethered

LEAP Runner [30] Soft 2020 Pneumatic Tethered

KTH Continuum

Quadruped

Soft 2020

Electro-mechanical

Untethered Table 1.1: Non-extensive comparision of work in quadruped robots

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1.5. RESEARCH QUESTIONS

1.5 Research Questions

It is essential that each soft robotic actuator be closed loop in order to ensure positional accuracy. Currently a majority of the work deals with open loop operation of continuum actuators, with less work relating to model based control [31]. Closed loop control of soft robots mostly relies on machine learn-ing based controllers [32][33]. However, this work uses model-based control design methods while the plant model is obtained using data-driven methods. Zolfagharian et al [33] use machine learning based controller for soft robots and conclude that applying other control algorithms developed using plant models may be feasible. This is in line with the suggested future work from Penning et al [34], who conclude that initial investigations into model based closed loop controllers have greatly improved positioning accuracy. For a quadruped robots it is essential that there is minimal deviation from the setpoint in order to reach the setpoint accurately and to prevent damage to the robot. It is also preferred that the lowest actuator effort be used in achieving the set point in order to maximize endurance. Therefore, it is proposed that a comparative study on applying two different controllers derived using both pole placement and LQR be perfomed. The comparison will be conducted on the basis of minimal set point deviation and minimal actuator effort. Based on this the first research question is formulated:

• In terms of minimal deviation from the set-point and actuator effort, how would pole placement and LQR based controllers for a wire driven continuum actuator compare?

Most soft quadrupedal robots are made of pneumatic and hydraulics, largely exhibit undulating and ambulating gaits [9][26]. Some of these tra-ditional robots are slow as the whole body of the robot is in contact with the ground and does not reflect the gait patterns of larger quadrupeds like dogs and cats. Larger quadrupeds exhibit gaits such as walk, run, pronk, trot etc. Therefore based on these, the second research question is formulated.

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1.6 Methods and Methodologies

The main methods and methodologies applied towards answering the re-search questions are discussed in this section. Rere-search question 1 is a quan-titative question, which seeks to compare the effectiveness of LQR and pole placement based controllers for a continuum actuator. This comparison will be made mathematically with the product of the total costs for deviation and actuator effort. The control method producing the lowest overall cost is deemed to be better.

The steps involved towards answering research question 1 are as follows:

• A literature survey on the various continuum actuators which are feasible for use in a quadruped robot

• Dimension, design and manufacture a continuum actuator which satisfies the requirements for a quadruped

• Design and manufacture the electronics for the continuum actuator and decide on an appropriate sampling time

• A literature survey on various modelling techniques of continuum actu-ators (mathematical and data driven modelling)

• Propose a model for the continuum actuator

• Design and test an LQR controller by iterating the values of Q which produces a local minima (or pareto front) for the actuator effort and deviation

• Design and test a pole placement based controller by selecting the pole locations which produces a local minima (or pareto front) for the actu-ator effort and deviation

• Compare the two controllers based on the product of the total costs for deviation and actuator effort

The second is a qualitative (also predictive) research question, which seeks to evaluate if a continuum actuator based quadruped can produce certain gaits which are commonly exhibited by rigid quadrupeds. While the answer to this question is a yes or no, the quality of the walk can be compared and deviations can be identified.

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1.7. ETHICS AND SUSTAINABILITY

The steps towards answering research question 2 are as follows:

• Manufacture 4 continuum actuators, which will be used as the legs of the quadruped robot

• Design and develop the body, electronics and controller topology for the quadruped robot

• Study the available literature for how various gaits behave and under-stand how these can be replicated or modified and applied

• Apply the gaits as a state machine or a similar method

• Provide evidence to prove that the quadruped can indeed execute the intended gaits

Based on the above methods and methodologies, the research question is answered and appropriate conclusions drawn.

1.7 Ethics and Sustainability

This thesis makes all attempts to provide all information and facts avail-able while presenting potential shortcomings. There exists numerous ethical concerns on work with robots, these have recently gained considerable impor-tance.

Testing methods for quadruped robots have received widespread criticism after videos showing employees of Boston Dynamics kicking robots in-order to display the effectiveness of their controllers emerged . This was argued to be ethically incorrect as it reveals the person kicking the robots to be cruel in their dispositions [35].

Ethical concerns exist in the area of soft robotics. This stems from the fact that during engagement with humans soft robots can evoke a sense of misplaced emotional attachment which can evoke a social and personal de-structive behaviour by users [36].

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1.8 Limitations and Delimitations

The experiments and solutions to the research questions answered in this thesis are subject to the following limitations:

• The maximum realistic sampling time of the electronics is limited to 50 ms due to the type of motors and communication overheads

• The motors can only processes position commands as these are provided as the inputs to the system

• There exists a noticeable (measurable) mechanical backlash in the sys-tem. This has the propensity to affect the results obtained.

The delimitations and assumptions in the experiments in this thesis are as follows:

• The connecting disks in the continuum actuator are assumed to be fully rigid

• The wires of the continuum actuator as assumed to be in-extensible • The continuum actuator is in-extensible along the direction of its axis,

this is achieved through directional stiffness

• The motor positions are assumed to model the model shape of the con-tinuum actuator

• Compressive loads (axial loads) are not considered as these loads cannot be opposed or controllable by the system

• Transitions between gaits are not considered

1.9 Organization and Work Distribution

This work is divided into 5 chapters. The first chapter details the funda-mental knowledge needed to understand the context and need for this study. This chapter also presents the methods used to answer these questions. The second chapter deals with the continuum actuator, its sizing, design and man-ufacturing, modelling and investigations into its control. The third chapter deals with the developed of a continuum actuator driven quadruped robot and

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1.9. ORGANIZATION AND WORK DISTRIBUTION

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Chapter 2 Soft Continuum Actuator

Cable driven hyper redundant continuum actuators have been around since the late 1990s [37]. However, these actuators were not soft in the true sense as these actuator were realised using rigid connecting plates. Soft rubber arms actuated using cables were developed by Wang et al [38]. These implemented a single section which could bend and deform. The soft continuum actuator presented in this chapter deals with a flexible multi-segmented cable driven actuator.

2.1 Sizing Requirement

This continuum actuator is to be deployed on a quadrupedal robot similar in size to a cat or small dog and therefore needs to be of a similar size. The leg length of a typical small dog is about 120 mm and the equivalent diameter of the legs is about 25mm [39]. The continuum actuator will be designed for a similar size. The legs consist of continuum actuators which can bend 90 degrees in each direction from the vertical and rotate 360 degrees along the horizontal direction. Large bending angles (>40 degrees) will allow for sitting and swimming motions in the future.

2.2 Mechanical Design and Fabrication

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CHAPTER 2. SOFT CONTINUUM ACTUATOR

Figure 2.1: A typical cable driven continuum actuator (regenerated from [40] IEEE ©[2013])

`

Figure 2.2: Actuator Design Parameters

2.2.1 Continuum Actuator Design

According to the sizing requirements above, the continuum actuator is designed for a length of 120 mm and a radius of 23 mm. However, in order to move the actuator, the wires must be pulled. The change in length of the wire creates the motion. The change of the wire length is created using a pulley connected to a motor. The diameter of the wire pulley is determined as follows:

The distance between the center of the wire and the center of the actuator is Rwire. If the leg can bend αleg degrees in each direction (as shown in Figure

2.2), the resultant change in the length of the wire is given by,

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2.2. MECHANICAL DESIGN AND FABRICATION

∆Lwire= 2 · 2π · αleg

360 ·Rwire (2.1)

It is assumed that the servo motor can rotate a maximum of θmotordegrees,

then the radius of the wire’s pulley Rpulley can be expressed as

Rpulley ≥

360 2π · θmotor

·∆Lwire (2.2)

The actuator tends to behave as a spherical mechanism as the tip of the actuator moves along the circumference of a sphere. This is possible because it is assumed that there is no longitudinal movement along the axis of the actuator. This lack of longitudinal movement is a result of directional stiffness. Through the manufacturing process, the stiffness of the actuator in various directions can be controlled.

The static tip positions of the actuator given a bending and rotational angle are specified by the following equations:

x = (L/B) × (1 − cos (B)) × (cos (R)) y = (L/B) × (1 − cos (B)) × (sin (R)) z = (L/B) × (cos (B))

(2.3)

Where L, B and R refer to the length, bending angle and rotational angle of the continuum actuator.

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Figure 2.3: Workspace of the soft actuator

Figure 2.4: Screw-less assembly of the motor and its associated components [11]

Since this design is weight sensitive, a screw-less assembly strategy has been adopted. All the parts have been designed in the transition to interference fit regime. This allows for the parts to be assembled without any screws. Potentially this could lead to low cost production as the overall part count

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2.2. MECHANICAL DESIGN AND FABRICATION

and cost per part is lower. An example of this type of design is the fit between the motor, motor housing, RC servo arm, wire pulley and potentiometer shaft as shown in Figure 2.4.

2.2.2 Fabrication

The continuum actuator is made of a flexible material (Young’s modulus 104

- 109

Pa), normally these flexible materials are either soft plastics, sili-cone or rubbers. Manufacturing with either rubber or silisili-cone requires the use of a mould [11]. This process is rather complicated considering the amount of time it would take to make a working mould and then cast the required parts. An additional weakness of this is that the quality of the parts needs an additional check. In order to avoid this cumbersome process, a strategy of 3D printing the actuator using TPU (marketed as Ninjaflex for 3D printing [41]) was adopted. Additionally, the process of 3D printing requires no human intervention, allowing for the parts to be manufactured without human super-vision. 3D printing of the actuator allows the entire manufacturing process to be on-demand as the same 3D printer can print various shapes and sizes with just a CAD file as the input.

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Figure 2.5: Rendered CAD model of the actuator

2.2.3 Actuation wire

An actuation wire is needed for bending the flexible parts. In general, a strong (higher yield and young’s modulus) wire with large flexibility is desired. The strength of the wire needs to be at least 100 times greater than the flexible material. This is essential as the wire is assumed to be non-extensible in mathematical models. Initially we made use of single stranded copper wire, but found this to be inadequate and failing very often owing to its low fatigue strength. In order to improve fatigue strength, we later made use of a wire rope of 0.72 mm diameter with 7 × 7 strands. This wire rope possesses a high fatigue strength and young modulus. It is also relatively soft and easy to bend this, we believe will fulfill our requirements.

2.3 Control Electronics Design and Fabrication

The motion of the wires which are used to move the bulk of the soft actuator is generated using motors. These motors are further controlled using various control electronics. The control electronics also derive and obtain feedback from position and current sensors. The data from these sensors is used to plan the control of the robot. This section describes and reasons the various electronics which have been implemented for use in the continuum actuator.

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2.3. CONTROL ELECTRONICS DESIGN AND FABRICATION

Figure 2.6: Comparison of the infill on the actuators

2.3.1 Electric Motor

The continuum actuator is driven by hobby grade position controlled RC servo motors. These types of motor were selected for their high power to weight ratio, speed of operation and high torque. These motors integrate gears and a position controller in the body. These motors are also relatively inexpensive and easy to control using standard PWM signals.

The RC servo motors require a PWM signal whose duty cycle corresponds to an angular position. The PWM signal is provided at a frequency of 50Hz and the duty cycle varies between 5% and 10%. These servo motors have internal digital position controllers which typically run at sampling speeds

<100Hz. The specifications of the motors used in this study are as follows:

• Servo HK47011MG:

– Motor Type: Coreless Titanium Geared

– Torque: 4.8V: 8.70 kg·cm

– Speed: 4.8V: 0.08 sec/60°

– Weight: 58.0 g

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• Servo TS-411MG:

– Motor Type: Brushed Alloy Geared

– Torque: 4.8V: 10.2 kg·cm

– Speed: 4.8V: 0.11 sec/60°

– Weight: 57.0 g

– Dimensions: 39.0 × 20.0 × 39.0 mm

These servo motors do not provide any feedback in terms of position or actuator effort. However, these are two important parameters needed for feed-back control. Therefore, external sensors are used to obtain these parameters.

2.3.2 Potentiometer

An analog potentiometer (trimmer pot) is used to obtain the position of the motor shaft. An analog potentiometer as opposed to rotary encoder is selected owing to its low profile, low cost and need for a single microcontroller pin. A single turn (PT15NV103A2020IPMS) is mounted along the motor shaft. A custom made PCB is used to mount the potentiometer. The total angle subtended by the shaft of the potentiometer is 234°. In this case an 8 bit ADC is used to sample the data. Therefore the position, independent of the resistance or the supply voltage is described by the following equation:

θ = M axAngle

2n₋₁ (2.4)

Where n is the resolution of the ADC (8 bit) and Max Angle is the maximum allowable shaft angle (234°) from the potentiometer

2.3.3 Current Sensor

Since the motor does not integrate a current sensor, external shunt resistors are added in order to sense current. The current in this case (DC motors) is directly proportional to the applied torque and relates to the actuator effort. A low side shunt resistor is connected between the ground of the servo motor and the ground of the power supply. The shunt resistor is connected to a TI INA2180 A2 IC which functions as a current sense amplifier. The current sense amplifier provides a fixed gain of 20 V/V. The output of the current

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sense amplifier is fed to a LP filter which is used to eliminate the ripple PWM signal from the motor. The first order R-C LP filter is dimensioned for a cut off frequency of 23.4 Hz and is realised using a 10kΩ resistor and a 0.68µF capacitor.

The output of the LP filter is directly fed into the pins of the 8 bit ADC which samples the signal. The current through the shunt resistor is described by the following equation:

i = ADCV alue

2n₋₁ ×

Vref Rshunt×Gain

(2.5)

Where i is the current through the motor, n is the resolution of the ADC (8

bit), ADCValue is the obatained sample from the ADC, Vref is the reference

voltage to the ADC (3.3 V), Rshunt is the value of the shunt resistor (0.01Ω)

and Gain is the voltage gain from the current sense amplifier (20 V/V).

2.3.4 Low Level Micro-controller Platform

An STM32 Nucleo-L47RG board is selected as the low level micro-controller platform. This microcontroller was selected for its low cost, large number of GPIO pins, Arduino compatible headers, large number of supported periph-erals and ease of use. The STM32L476RG integrates an ARM Cortex M4 processor running at 80 MHz. The STM32 possesses 16 inputs channels on its ADCs and integrates 2 advanced timers which can be use for generat-ing accurate high resolution PWM signals [43]. Given these functions, this microcontroller could in the future be deployed to control 2 continuum actua-tors. The microcontroller collects position and current data from the sensors through its peripherals and transmits them to the high level micro-controller platform. Concurrently, the STM also deploys the actuator commands it re-ceives. The communication between the low level and high level platform is performed using the UART communication standard.

2.3.5 Printed Circuit Board (PCB)

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Figure 2.7: PCB and Micro-controller for Controlling a Con-tinuum Actuator

2.3.6 High Level Micro-controller Platform

The high level micro-controller is implemented using a TI C2000 F28379D Delfino board [44]. The C2000 was selected for its low cost, real time external mode compatibility with Simulink, Control Law Accelerator (CLA) and full peripheral compatibility with Simulink. The dual core nature of the C2000 is promising as the control tasks can be split between the different cores of the micro-controller, this allows for true parallelization.

2.3.7 Software

Low Level Software Overview

The software for this system is implemented on different levels. The first layer of software is implemented on the low level microcontroller. The software in the STM32 is implemented in C. The software reads the potentiometer position from the ADC and using a DMA channel. The same is done for reading the voltage input from the current sensors. The low level controller receives control inputs over serial(UART) from a high level controller. Once an incoming UART signal is recognized by the microcontroller an interrupt is triggered. After the interrupt is triggered, the microcontroller starts reading from the UART port. The data from the UART port is unpacked and checked. Contained in this data are the position commands destined to the servo motor. The bounds (saturation) of the commands are checked following which, they

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are converted into a PWM duty cycle and then deployed through the timer peripheral. The detailed code is available in Appendix C: Code Base.

2.3.8 High Level and Calibration Software Overview

A simple python tool was developed to test and calibrate the zero position of the continuum actuator upon the completion of the mechanical assembly. This tool directly runs on a computer and employs the use of a GUI to enable ease of use. This tool makes use of the ’PySerial’ package and communicates with the microcontroller over USB emulated serial. The GUI tool was designed and developed using the ’PyQt’ package. Figure 2.8 shows the GUI developed for calibration and testing. The code for this has been provided in Appendix C: Code Base.

Figure 2.8: The GUI developed for calibration and testing

Once the actuator was assembled using the GUI, the data collection and control were performed using Simulink based code generation and develop-ment. A Simulink package for the Texas Instruments C2000 F28379D was used. This package supports most function of the microcontroller which in-cludes ADCs, UART, DMA, Interrupts, GPIO among a few.

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bit termination identifiers. The identifiers help the low-level controller iden-tify the start and end of the message. A similar sequence is implemented for receiving position and current data from the low-level microcontroller. The closed loop controller for the system is implemented through simple blocks. An indicative image of the Simulink based code has been provided in Appendix B.

2.4 Assembly

Figure 2.9: Rendered exploded view of the continuum actuator and its supporting accessories

In order to test the design of the actuator, an assembly of the actuator was made. The motor is embedded in 3D printed motor holder, this is mounted on the base through an interference fit. The PCB mount was fit inside the PCB base which was later fit into the actuator base. The motor and potentiometer are connected through the wire pulley and potentiomenter shaft. Since the continuum actuator is soft, a supporting structure is glued to the actuator and the this part is connected to the base with screws, the screws are needed for

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2.5. MODELLING AND PARAMETER ESTIMATION

adjusting the assembly. The wire rope is fastened to the end of the continuum actuator and is glued in place. The other end of the wire is loaded on the wire pulley and fastened and glued on. An image of the exploded assembly view of the actuator is shown in Figure 2.9.

It is essential to note that both the motor and the potentiometer have a limit to the maximum extent of their positions. The motor rotates 120 degrees and the potentiometer rotates 234 degrees. When assembled, the same position for the motor must be used to ensure consistency and a safe working range for the potentiometer.

Additionally, the tension on the continuum actuator needs to be adjusted when mounting the wire on the pulley. The tension on all the three cables needs to be proportional and the cables taut for the assembly to result in a horizontal neutral position.

2.5 Modelling and Parameter Estimation

Modelling and parameter estimation for the actuator are important for closed loop control. In theory, better models lead to better controllers. How-ever, modelling soft and elastic segments can be quite challenging owing to flexibilities and multiple degrees of freedom of the system.

The actuator consists of 2 degrees of freedom which are of interest to us, these are bending and rotational angles. The bending angle α, is the central angle corresponding to the arc formed when the soft actuator is bent, and rotational angle β, represents the orientation of the soft actuator projected to the plane. When the actuation wires are pulled, the actuator deforms in both bending angle and rotational angle. The equation between pulling of the wires and two angles are given in Eq 2.6.

∆La = Rwire·α · cos(β) ∆Lb = Rwire·α · cos(β + 2 3π) ∆Lc = Rwire·α · cos(β + 4 3π) (2.6)

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model involving all intermediate states. The numerous possible mode shapes renders this type of model unusable in most embedded and real time con-trol applications as the size of the state matrix increases with increase in the number of nodes.

Second, when a continuum actuator is fabricated using 3D-printing using flexible material the complex structure and multiple degrees of freedom makes it difficult to estimate the parameters of the actuator. Additionally, there exists a backlash between servo motor and potentiometer and this introduces non-linearity in the system. Added to this, the servo motor and potentiometer have maximum angles, which cannot be exceeded. This saturation adds non-linearity to the system.

Third, due to the lack of proprioceptive position sensors, the true shape of the continuum actuator when performing real time control without the use of exoceptive sensors. Due to these reasons a practical model with proprioceptive control, a data driven model using the potentiometer position sensors and current sensors is more feasible for this scenario.

In the following sections, the calibration of the potentiometer and motor will be explored. Following that the development of the data driven model will be explained and the development of various controllers.

2.5.1 Potentiometer and Motor Calibration

Under normal circumstances, the position of the potentiometer and the resistance are a linear function. However, due to the design of the motor itself and the fact that connecting parts between the motor and the potentiometer may be slightly twisted, the entire system will have system error and backlash. To solve this problem, we calibrate both motor and potentiometer together and develop a look-up table. The potentiometer and motor outputs have been provided as a graph in Figure 2.10.

For the front motor, all the curves have similar slopes, which means the potentiometer has the similar performance and have a linear relationship with the motor rotation angle. However, due to the error in the assembly of the motor and the potentiometer, the value of each potentiometer cannot com-pletely correspond to the rotation angle of the motor , which makes some potentiometers have a dead zone, that is, the rotation angle of the motor does not start from 0. Compared with Front motors, Rear motors performs better in uniformity. But there is a slightly difference. Since the two motors rotate

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2.6. DYNAMIC PERFORMANCE OF THE SYSTEM

in opposite directions, the curve of the front motor is upward and the curve of the rear motor is downward.

Figure 2.10: A plot of the Motor Positions and Potentiometer Position

2.6 Dynamic Performance of the System

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load from a continuum actuator and without the addition of a load will be studied. The motor is provided with a step input of 50 degrees and the step response of the motor under both conditions were recorded as seen in Figure 2.11.

The step response is shown in Figure 2.11. From the figure it can be observed that the motor position has a unity gain (the state of the output at infinite time matches the input). Additionally, the settling time (time taken to get within 10% of the final value) for a single motor without a load is about 0.4 second and there appears be no overshoot, this proves that the motor has reasonable position control performance.

However, when the motor is connected to the continuum actuator, the settling time rises and is greater than 2 seconds. This is due to the influence of the restoring force in the actuator which grows as the displacement is increased (assuming that the actuator is a spring). From the graph it is also seen that the curve approximately resembles an inverted logarithmic curve when the load is added. The logarithmic nature can be explained by that fact that the spring stiffness varies by the square of the position (non linear spring).

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Time(s) 0 10 20 30 40 50 60 Angle (deg)

Step response of the motor with and without a load

Reference Motor with Load Motor without Load

Figure 2.11: Step response of the motor

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2.6. DYNAMIC PERFORMANCE OF THE SYSTEM Bending & Rotation Reference To Motor Reference (ABC) Motor + Actuator Bending Rotation

ABC Position,Current

Figure 2.12: Structure of system for model estimation data collection

Three of these motors are combined to form the actuator. These motors act antagonistically to each other and there also exists a restoring force due to the stiffness of the actuator. Since, the motors can influence the perfor-mance of each other through the actuator, this leads to a Multiple Input Multiple Output (MIMO) system. Therefore, the input to each motor must take the antagonistic nature into account. Through Figure 2.11, it can be observed that the addition of a load significantly changes the performance of the motors. When three of these motors are combined for antagonistic use, an unaccounted change in performance can lead the motors to damage them-selves or waste significant energy to during high speed dynamic operations. In order to alleviate the effects of this, a global controller which takes into account the current state of the motors while providing reference inputs is deemed necessary.

The input to the motors are specified in terms of bending and rotation, and these are converted to input angles for the motor in accordance with Eq 2.6. The structure of input and output measurements are shown in Figure 2.12. In the figure A, B, C correspond to the inputs of three motors.

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CHAPTER 2. SOFT CONTINUUM ACTUATOR 0 10 20 30 40 50 60 Time (s) -20 -10 0 10 20 30

Angle Observed (deg)

Actuator Motor Performance

Motor A Motor B Motor C 60 70 80 90 100 110 120 Time (s) -20 -10 0 10 20 30

Angle Observed (deg)

Actuator Motor Performance

Motor A Motor B Motor C

Figure 2.13: Actuator Motor Performance

In the collected data in Figure 2.13 it can be observed that around times 0, 55 and 82 seconds there are transitional states. In order to estimate the model the data between time 40 and 70 seconds is taken, as shown in Figure 2.14. This will serve as the model fitting data set. The estimated model will

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2.6. DYNAMIC PERFORMANCE OF THE SYSTEM

then be applied on the whole input data set and the accuracy of the model will be compared. -20 -10 0 10 20 30 PositionOutA -15 -10 -5 0 5 10 15 20 PositionOutB -20 -15 -10 -5 0 5 10 15 20 PositionOutC 25 30 35 40 45 50 55 60 65 70 75 -30 -20 -10 0 10 20 30 AngleRefA 25 30 35 40 45 50 55 60 65 70 75 -20 -15 -10 -5 0 5 10 15 20 AngleRefB 30 40 50 60 70 -20 -10 0 10 20 AngleRefC

Data driven model training data

Time (seconds)

Angle(deg)

Figure 2.14: The data used to fit the model

A state space model was estimated using the MATLAB function ’ssest’. This function takes in the data set (input and output wave forms), model order, form of the model and the sampling time as the input. Based on these a state-space model is estimated. The method used by ’ssest’ to estimate the model according to the MATLAB web page is ’non-iterative subspace approach or an iterative rational function estimation approach’. The model was set to a canonical form so that the observed states are the outputs of the system (C matrix is an identity matrix). Also, a disturbance free model was requested (disturbance matrix K is zero). Using this approach, the model order could be iterated on. Various model orders were experimented with and the result of these are shown in Table .

Motors Order = 3 Order = 6 Order = 10

A 85.62% 89.25% 88.41%

B 82.99% 84.32% 87.2%

C 81.5% 84.71% 87.6%

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Based on the table it is observed that the increase in accuracy is marginal between different model orders. Therefore in order to prevent over-fitting a simple model of order 3 will be taken. Based on this model, the same input signal is provided to the model and its performance is obtained. This performance is shown in Figure 2.15

-20 -10 0 10 20 30 PositionOutA

Real System (PositionOutA) Modelled System: 85.62% -20 -10 0 10 20 PositionOutB

Real System (PositionOutB) Modelled System: 82.99% 20 40 60 80 100 120 -30 -20 -10 0 10 20 30 PositionOutC

Real System (PositionOutC) Modelled System: 81.5%

Comparision of the system and model performance

Time (s) (seconds)

Angle (deg)

Figure 2.15: Input data applied to the estimated model

Based on this figure it can be observed that the model responds well to the inputs and is almost indicative of the data collected from the system.

2.7 Controller Outline

Although the system meets design requirements without feedback control when there is no external load, the same may not be the case when an external load is applied. If an external load is applied, the current state of the motors is not used in determining the global response of the system.

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2.7. CONTROLLER OUTLINE

Based on the model of the system developed, two controller synthesis types will be tested. A pole placement based controller and an LQR based on con-troller, since there can be numerous possibilities for the controller in terms of poles for the pole placement controller and in terms of the Q matrix for the LQR. A linear regression based approach is adopted for minimizing the con-troller effort and the deviation from the set-point. The steps for this method is as follows:

• Set the location of poles or Q matrix values to be iterated

• Based on these, obtain the controller matrix K satisfying the respective equation for closed loop control

• Simulate the system given inputs and obtain the data • Now, estimate the RMS deviation from the set-point

• Find the controller effort (defined as the integral of acceleration) • Change the location of the poles and the Q matrix and iterate

• Plot these on a graph with RMS deviation as the X axis and controller effort as the Y axis

• Find the local minimum, this point provides the best controller

• If a local minimum can not be obtained, change the limits of the iteration and try again

A general outline of the controller architecture is given in Figure 2.16.

Bending & Rotation Reference To Motor Reference (ABC) Motor + Actuator Bending Rotation ABC Position, Current Bending and Rotation Output Kr K

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The controller here consists of two parts, these are the the controller gain matrix K which satisfies the Ricati equation for LQR and close loop pole lo-cation for pole placement. Additionally an input scaling gain matrix Kr is needed to scale the input signal in order to obtain a step response of 1. For a system without an integrator the feed-forward input scaling gain matrix is calculated by the reciprocal of the DC gain in order to obtain a step response of 1 [45]. In this case the problem presented can be viewed as three individual systems which are coupled. Therefore the steady performance of each sys-tem can affect the steady state performance of the other two syssys-tems. The gain scale matrix is converted into a diagonal matrix because the system is canonical and has distinct eigenvalues [46].

The input to the system is obtained from the bending and rotational angle set-points which are transformed into motor inputs. Note that the actual final states of the system, bending and rotation cannot be sensed by the system. These can be inferred using real time motor position.

2.8 LQR Based Controller and Results

The state space representation for a MIMO system are given by the fol-lowing equation,

˙x = Ax + Bu (2.7)

y = Cx + Du (2.8)

AController = A − B ∗ K (2.9)

u = −Kx (2.10)

Where, A represents the state matrix and B represents the input matrix, C is the output matrix and D is the feed through matrix. In our case, matrix C is an identity matrix and D is zero.

An LQR system minimizes the quadratic cost function subject to the state space system and the cost function is given by,

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2.8. LQR BASED CONTROLLER AND RESULTS

J(u) =

Z ∞

0 (x

T_{Qx + u}T_{Ru + 2x}T_{N u)dt} _(2.11)

In MATLAB, a single command ’lqr’ performs these and provides the con-troller with the gain matrix K which satisfies this equation. The input to the command is the model, Q and R matrices. Since the influence of state parameters are significantly greater than the influence of our inputs, in our case we fix R = 0.01 and then vary Q (between 0.001 to 5 in steps of 0.001) as an identity matrix and assigning equal weights to the elements of the ma-trix. By doing this, various values for the Q matrix could be tested. Since this is a coupled system, the co-dependence between R and Q is high. Due to this, changing any of one of these can influence the system in terms of the other. Following the steps as discussed in controller outline, the plot of the RMS error and the controller effort are shown in Figure 2.17. The curve has a distinct kink and shows a point where there is a decrease in both the RMS error and actuator effort.

18.56 18.58 18.6 18.62 18.64 18.66 18.68 18.7 18.72 RMS Error (deg) 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760

Acuator Effort (deg/sec)

Plot of the RMS Error and Actuator Effort

Figure 2.17: Plot of RMS error and Actuator Effort

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CHAPTER 2. SOFT CONTINUUM ACTUATOR -30 -20 -10 0 10 20 30 To: Out(1) -40 -20 0 20 40 To: Out(2) 0 10 20 30 40 50 60 -40 -20 0 20 40 To: Out(3) Simulated LQR controller Time (s) (seconds) Angle (deg) -20 0 20 40 To: Out(1) -40 -20 0 20 40 To: Out(2) 70 80 90 100 110 120 -40 -20 0 20 40 To: Out(3) Simulated LQR controller Time (s) (seconds) Angle (deg)

Figure 2.18: Simulated LQR controller

From the simulated closed loop response in simulation in Figure 2.18, it can be observed that the response time for the signal has been increased.

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2.9. POLE PLACEMENT BASED CONTROLLER AND RESULTS

This is evident by the fact that there is very little observed overshoot or deviation. Some deviation is observed at the start of the curve, as the motors are reaching their states. However, it is essential to that these simulations are made in continuous time, but the hardware is a discrete system with a low sampling time (0.05 s). In order for the system to be able to follow the reference, a realistic input must be supplied, keeping in mind the sampling time.

This controller was tested in hardware with fast reference signal approach-ing its samplapproach-ing time. This was done to evaluate the performance of the controller given a fast reference signal. The plot for this is provided in Figure 2.19. From the plot it can be observed that the system can follow the refer-ence. There exists a delay in the actual system following the reference, this delay is almost the length of two sample times. This can most likely be the result of a two way communication delay caused by the sample time. Addi-tionally, this may be causing some overshoot, as it can be seen that there is a 5% overshoot with respect to motor A.

137.5 138 138.5 139 139.5 140 140.5 141 Time (s) 20 30 40 50 60 70 80 90 Angle (degrees) Hardware Implemented LQR Motor A Response Motor B Response Motor C Response Motor A Reference Motor B Reference Motor C Reference

Figure 2.19: Hardware implemented LQR controller

2.9 Pole Placement Based Controller and

Results

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be directly controlled. The poles of the system highlight an important issue, which is that the closed loop poles need to be placed at a distance of 10 to 30 times between each other. Therefore, when a closed loop controller is being developed, the new poles will be placed 10 times further away from each other. Based on the method specified in controller outline, the closed loop poles were iterated between -1 to -10 in steps of -1. The result of the iteration based on the RMS error and actuator effort is shown in Figure 2.20.

60 80 100 120 140 160 180 200 220 RMS Error (deg) 4000 4500 5000 5500 6000 6500 7000 7500 8000

Actuator Effort (deg/s)

Pole placement RMS error vs actuator effort

RMS error vs Actuator effort

Figure 2.20: Pole Placement RMS Error vs Actuator Effort

Through this graph it can be observed that there is no distinct minimum, as the minima in this case occurs at -20. It is however, essential to note that moving the poles any further may impact the closed loop performance when the sample time is taken into account. Since the sample time is 0.05, this corresponds to a pole location of -20. This is fastest possible system configuration.

Based on the fastest possible pole, this was applied to the simulation model and the results are shown in Figure 2.21.

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2.9. POLE PLACEMENT BASED CONTROLLER AND RESULTS -30 -20 -10 0 10 20 30 To: Out(1) -40 -20 0 20 40 To: Out(2) 0 5 10 15 20 25 30 -40 -20 0 20 40 To: Out(3)

Linear Simulation Results

Time (seconds) Amplitude -30 -20 -10 0 10 20 30 To: Out(1) -40 -20 0 20 40 To: Out(2) 30 35 40 45 50 55 60 -40 -20 0 20 40 To: Out(3)

Linear Simulation Results

Time (seconds)

Amplitude

Figure 2.21: Simulated Closed Loop Pole Placement System

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when this controller was tested in hardware, it was observed that the steady state gains were quite high. These remain unexplained and it is speculated that this might have to do with the sample. Therefore, the results of the testing the closed loop pole placement based controller remain inconclusive.

2.10 Discussion and Controller Comparison

It is observed through the preceding paragraphs that the pole placement based controller could not be tested on the hardware due to various reasons. Additionally, the minimal RMS error and actuator effort for the two con-trollers were found to be 4.1733 × 103

and 1.55 × 103

for pole placement and LQR based controllers. Therefore, it can be concluded that the performance of a controller synthesised through LQR is better than that of a controller synthesised through pole placement.

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Chapter 3 Soft Quadruped Platform

3.1 Chapter Overview

This chapter details the manufacturing of the soft quadrupedal robot and the testing of various gaits on this robot. This chapter is split into mechan-ical design and manufacturing, electrmechan-ical design and manufacturing, walking pattern generation and gait performance.

3.2 Mechanical Design and Manufacturing

A rendered drawing with the four legs and the body is shown in Figure 3.1. The body of quadruped platform consists a spine while holds the actuators together. The spine of the quadruped is made of laser cut acrylic plastic. Four continuum actuators as described in Chapter 2 were manufactured. These are then mounted on the acrylic frame. The front legs are placed at a distance of 150mm from each other. This spacing is provided in order to ensure that the legs do not come in contact with each other during normal motion. Also, the distance between the front and the rear legs is set to be 30mm. These dimensions are in line with that of a small animal.

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CHAPTER 3. SOFT QUADRUPED PLATFORM

Figure 3.1: Overall view of the soft quadruped platform

Figure 3.2: A fully assembled and mounted quadruped

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3.3. ELECTRICAL DESIGN AND MANUFACTURING

It is essential to note that before testing the quadruped on the ground, an analysis of the spine and load bearing capacity need to be carried out.

3.3 Electrical Design and Manufacturing

An overview of the electrical design is provided in Chapter 2 and Figure 3.3. For the electrical parts of the quadruped, a similar approach is followed. A high level controller (TI C2000 F28379D) running simulink runs the closed loop control of each of the continuum actuators. The same micro-controller also manages the global control of the quadruped. This micro-controller is also connected to a PC running Simulink, where real time monitoring and tracking can be performed.

Two low level controllers, each managing the front and read legs of the quadruped are made of STM32 based micro-controllers, these communicate over UART and receives commands from the high level micro controller. The low level micro-controllers are connected to PCB which also serve as the power distribution boards to the servo motors. An image of a low level controller with all its parts has been indicated in Dual Actuator Control PCB and Accessories. The code for the low level controllers has been developed in C and is provided in Appendix C: Code Base.

The wiring and connection overview for the low level and high level micro-controllers has been shown in Figure 3.3. In the figure in can be seen that the high level micro-controller communicates the parameters with Simuliunk in Real Time.

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Continuum Actuator

Embedded Microcontroller (STM32 Nucleo L476RG)

ADC Peripheral

Interrupt Based Serial Communication with Header and Termination Encoding and Decoding ST Link Programmer

USB and Onboard 3.3V Regulator

Front Legs Continuum Actuators Front Legs PCB

Shield

TI C2000 F28379D

Board Simulink HostComputer

Power over USB Parameter Data and Display Data (SCI A)

USB Simulink Front End Display (External Mode) Power over USB External +5V DC +5 VDC Serial COM Port Front Legs Communication (SCI2) Rear Legs Communication (SCI-D)

Rear Legs PCB Shield

Common Ground UART Current Sense Ampliﬁers RC Low Pass Filter +3.3 VDC

Servo PWM Timer Peripheral

Servo Motors Current Shunt

Resistors _{Position Sense}

Potentiometers

Mains AC

Interrupt Based Serial Communication with Header and Termination Encoding and Decoding ST Link

Programmer USB and Onboard 3.3V

Regulator

ADC Peripheral

Servo PWM Timer Peripheral RC Low Pass Filter Current Sense Ampliﬁers Current Shunt

Resistors Servo Motors ST Link

Programmer USB and Onboard 3.3V

Regulator

Interrupt Based Serial Communication with Header and Termination Encoding and Decoding

ADC Peripheral

Servo PWM Timer Peripheral RC Low Pass Filter ST Link Programmer USB and Onboard 3.3V Regulator

ADC Peripheral

Servo PWM Timer Peripheral RC Low Pass Filter Current Shunt Resistors ST Link Programmer USB and Onboard 3.3V Regulator

ADC Peripheral

Servo PWM Timer Peripheral RC Low Pass

Filter

Current Shunt

Resistors Position Sense Potentiometers Servo Motors

Front Legs Continuum Actuators +3.3

VDC Front Legs PCB

Shield Rear Legs PCB Shield

External +5V DC UART Common Ground Rear Legs Communication (SCI-D) Front Legs Communication (SCI2)

Parameter Data and Display Data (SCI A) Power over USB

Embedded Microcontroller (STM32 Nucleo L476RG)

TI C2000 F28379D Board

Figure 3.3: Electronics hardware Overview of the Quadruped

3.4 Gait Pattern Generation

Gait refers to the pattern of limb movement during locomotion. While the exact definition of gait can vary, general consensus exists on the fact that gait can refer to a parameter called ‘foot strike’. Where ‘foot strike’ can refer to the contact made with the ground in a specific sequence [47].

One advantage of a quadruped robot is that they can carry out gait plan-ning, enabling them to adapt to various surfaces and environments. There-fore, they can walk on irregular terrains using special gaits. Based on the stable controller for each leg that we have already designed, we can addition-ally introduce a gait pattern at a global level in our quadruped robot. The gait pattern generator, generates input signals for each of the legs. In more complex quadrupeds, this manifests itself as a MIMO controller, typically im-plementing Model Predictive Control (MPC) with gait planning. However, in order to generate simple walking motions, a sinusoidal waveform with a variable amplitude is supplied to the legs.

In our case, phase shifted sinusoidal signals for changing the bending of legs at a fixed rotational angle is provided. This allows the quadruped to flex and bend in the direction of walking. An illustration of this logic level is

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3.5. GAIT PERFORMANCE

provided in Figure 3.4. The sinusoidal phase shifted signal sequence supplied to the legs of the quadruped are shown in Table 3.1. In the walk gait opposing legs are synchronous while in the galloping gait, the two front legs and the two back legs are synchronous.

Front Leg 1 Local Controller Front Leg 2 Local Controller Rear Leg 1 Local Controller Rear Leg 2 Local Controller Oscillator

Figure 3.4: Oscillator based generation of walking sequence

Leg Walk Gait (Phase Shift) Gallop Gait (Phase Shift)

Front Left 0° 0°

Front Right 90° 0°

Rear Left 0° 90°

Rear Right 90° 90°

Table 3.1: Gait sequence phase shifts

3.5 Gait Performance

The two common gaits are walking and galloping. The walk gait is a slow, four-beat, rhythmic pace of distinct successive feet contacts. The sequence for walking on four legs is left rear, left front, right rear, right front. Alternately two or three feet may be touching the ground at the same time[48]. Based on the above theory and movement sequence, we designed a walk gait for the quadruped robot. In this case the time required to complete a full cycle of the gait was 4 seconds. A video of the walking was recorded and snapshots are provided in the form of figures in the order of time. The forward direction is the left side of the image.

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Figure 3.5: Walking gait

Figure 3.6: Galloping gait

Another gait is called galloping. It is similar to when an animal runs. It can be divided to three parts. The legs in front move in the same direction and and in the opposite direction to rear legs. In the first step the two front legs will stretch to the front, while two rear legs stretch back. This time the whole robot starts moving. Then four legs start to move in the opposite direction.

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3.6. CONCLUSIONS

The galloping can be on the front or back side, depending on which is the last foot to leave the ground [48]. The figures of galloping gait are are shown in Figure 3.6. In this case the time required to complete a full cycle of the gait was 2 seconds. Since, these tests were performed without a load on the robot, the fastest observed leg movement cycle was about 1.3 seconds.

3.6 Conclusions

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Chapter 4 Discussions and Conclusions

Quadruped robots can largely traverse uneven terrain as opposed to wheeled robots. These robots are however, limited by their compliance to terrain owing to rigidities. Soft quadrupeds present an advantage in terms of compliance, but are generally tethered. This work aimed at producing an untethered wire driven continuum actuator based soft quadrupedal robot.

The present work focused on developing wire driven continuum actuators for the purpose of walking. Pole placement and LQR based controllers were implemented on these actuators. Finally, these actuators were deployed to a quadruped and various gaits were evaluated.

Modelling and control of soft actuators can be particularly challenging as a result of their hyper-redundant nature. This hyper redundancy results in numerous bending possibilities when a fixed load is applied axially to the actuator. Additionally, the system also consists of various non-lineartites. These are a result of manufacturing tolerances, backlash and the inherent non linear nature of the elastic core. However, with a large enough set of data, these non-linear elements of the model can be linearized.

Continuum Actuator Based Soft Quadruped Robot

Continuum Actuator Based

Soft Quadruped Robot

SESHAGOPALAN THORAPALLI

MURALIDHARAN

Abstract

Sammanfattning

Acknowledgements

Contents

List of Figures

List of Tables

Acronyms

Chapter 1

Introduction

1.1

Overview of Quadruped Robots

1.2

Overview of Soft Robots

1.3

Overview of Continuum Actuators

1.4

Proposed Soft Continuum Quadruped

1.5

Research Questions

1.6

Methods and Methodologies

1.7

Ethics and Sustainability

1.8

Limitations and Delimitations

1.9

Organization and Work Distribution

Chapter 2

Soft Continuum Actuator

2.1

Sizing Requirement

2.2

Mechanical Design and Fabrication

2.2.1

Continuum Actuator Design

2.2.2

Fabrication

2.2.3

Actuation wire

2.3

Control Electronics Design and Fabrication

2.3.1

Electric Motor

2.3.2

Potentiometer

2.3.3

Current Sensor

2.3.4

Low Level Micro-controller Platform

2.3.5

Printed Circuit Board (PCB)

2.3.6

High Level Micro-controller Platform

2.3.7

Software

2.3.8

High Level and Calibration Software Overview

2.4

Assembly

2.5

Modelling and Parameter Estimation

2.5.1

Potentiometer and Motor Calibration

2.6

Dynamic Performance of the System

2.7

Controller Outline

2.8

LQR Based Controller and Results

2.9

Pole Placement Based Controller and

Results

2.10

Discussion and Controller Comparison

Chapter 3