Stability Enhancement of Reconfigurable Robots

M A S T E R ' S T H E S I S

Stability Enhancement of Reconfigurable Robots

Tawon Uthaicharoenpong

Luleå University of Technology Master Thesis, Continuation Courses Advanced material Science and Engineering

Department of Space Science, Kiruna

2008:115 - ISSN: 1653-0187 - ISRN: LTU-PB-EX--08/115--SE

Tawon Uthaicharoenpong

Stability Enhancement of Reconfigurable Robots

Thesis submitted in partial fulfillment of the requirement for the degree of Master of Science in Technology

Espoo, July 31, 2008

Supervisors:

Professor Aarne Halme Professor Kalevi Hyyppä Helsinki University of Technology Luleå University of Technology Instructor:

Professor Peter Jakubik

Helsinki University of Technology

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First I would like to thanks Professor Aarne Halme, for gave me chance to explore the thesis topic of my interest and also to Kalevi Hyyppä for his kind guidance on my thesis improvement.

I would like to thanks my instructor, Peter Jakubic for his broad guide line of researching and implementing this thesis work, and Tomi Ylikorpi for prove and suggestion my mechanical design and implementation, and without incredible craftsmanship of Tapio Leppänen the robot couldn‟t be built.

Lots of thanks to all Spacemaster colleague here at TKK, Masaki, Vicky, Richard(Bui), Jans, Paavo, Felix, Khuram, Fahruk, for good time and effort to get us go through many things during the year and especially to Jans for his patience advice on programming, mathematics and helpful advice.

Tawon Uthaicharoenpong

Otaniemi, July 31, 2008

iii

Author: Tawon Uthaicharoenpong

Title of the thesis: Stability enhancement of reconfigurable robot

Date: July,31, 2008 Number of pages: 79

Department: Automation and System Technology

Professorship: Automation Technology Code: AS-84

Supervisors: Prof. Aarne Halme

Instructor: Prof. Peter Jakubik

Future planetary exploration missions will require mobile robots to excess challenging terrain such as rocky areas, steep slopes or loose soil types which make robots susceptible to losing stability leading to rollover or entrapment.

So far this problem have been proposed to be solved by the use of reconfigurable robots, robots that can reconfigure themselves, these robots have an advantageous ability to reconfigure themselves to optimize their performance according to the surrounding area, i.e. to adjust wheel diameter according to soil conditions to optimize wheel-ground traction, to adjust shoulder joint angles to keep the center of gravity within a suitable area thus increasing tip over stability.

To define and give a measure of stability, which has no official unit and theory yet, various kinds of stability measures have been studied and discuss about the drawback and generality of each measure. The most suitable measure selected to be implemented in this thesis work is the force-angle stability measure.

The conceptual design of the robot prototype built with the help of a 3D mechanical design program, which later was used to find many important parameters of the robot, afterward it was then manufactured within the TKK Automation laboratory facility. It is a four wheeled skid-steer robot platform with an inverted pendulum mounted on top.

Control software has been developed both for the local controller (AT90CAN128 from Atmel), where the manipulator position control method is run, as well as on the PC where the implementation and development of force-angle stability measures take place using MATLAB.

The robot prototype was then tested to measure the performance of the robot and to investigate how the system reacts to various test method. The test data was collected and analyzed and was proven to significantly enhance the stability of the robot.

Keywords: Stability enhancement, Reconfigurable robot, Exploration robot

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Contents ... iv

Chapter 1 Introduction ... 1

1.1 Current mission and future trends ... 1

1.2 Reconfigurable robots ... 4

1.3 Thesis scope ... 4

1.4 Thesis structure ... 4

Chapter 2 Literature Review ... 5

2.1 Brief history of space exploration ... 5

2.2 Example of reconfigurable robots ... 8

2.2.1 Sample Return Rover (SRR)... 8

2.1.2 Reconfigurable wheel ... 10

2.3 Type of stability margin ... 11

2.2.1 Center of gravity and zero-moment point based stability margin ... 11

2.3.2 Energy based stability margin... 16

2.3.3 Force-angle Based Stability Measure ... 22

Chapter3 Hardware Design and Development ... 25

3.1 Mechanical Design ... 25

3.1.1 Mobile platform ... 27

3.1.2 Inverted pendulum ... 28

3.2 Electronics Design ... 29

3.2.1 Microcontroller ... 29

3.2.2 Sensor... 30

3.2.3 Motor Driver ... 32

Chapter4 Software and Control ... 33

4.1 Microcontroller ... 33

4.2 Algorithm development and simulations studies ... 37

4.2.1 Brute force method ... 38

4.2.2 Look up table ... 41

4.2.3 Optimization Method ... 42

Chapter 5 Test and Test Result ... 45

5.1 1

Test: Center Of Gravity Test ... 45

5.2 2

Test: Stability Enhancement ... 46

5.3 3

Test: Going Up and Down Inclined Ramp ... 48

5.4 4

Test: U shape Drive on inclined plane ... 49

5.5 5

Test: Outdoor test ... 50

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Appendix A : Test result of Stability Enhancement ... 57

Appendix B : Electronics schematics ... 60

Appendix C : Mechanical Drawing ... 65

Motor specification ... 68

Reference ... 71

vi ADC Analog to Digital Converter

COM Center Of Mass

COG Center Of Gravity

CAD Computer-Aided Design

CAN Controller Area Network

ESA European Space Agency

JPL Jet Propulsion Laboratory LSB Least Significant Bit

MER Mars Exploration Rover

MOSFET Metal Oxide Semiconductor Field Effect Transistor MSB Most Significant Bit

NASA National Aeronautics and Space Administration

PC Personal Computer

PWM Pulse Width Modulation

PID Propotional Integral Deriviative

SRR Sample Return Rover

TKK Helsinki University of Technology

ZMP Zero Moment Point

1 Chapter 1 Introduction

To be able to establish permanent settlement for manned missions to other planets and to pave the way for humanity to reach outer space and beyond the solar system, the information about the planet to be visited has to be gathered. To be able to plan and develop the technologies needed to live and work safely in space.

1.1 Current mission and future trends

In 2004, NASA sent twin exploration rovers, named Spirit and Opportunity, act as a geologist on the red planet in pursuit of past water activity. The rovers were equipped with tools for close-up inspection of a diverse collection of Martian rock, each rover possessing the equivalent tool of a human geologist walking on the surface of Mars.

Included is RAT, Rock Abrasion Tool, which serves the purpose of a geologist‟s rock hammer to expose the inside of rocks. Although the rovers did not have the ability to detect life directly, they offer information on the habitability of the environment and the planet‟s history.

Figure 1. Robotic arm reaching to examine the rock with tools on the arm. Credit NASA

Figure 2. Shadow of rover Opportunity in Endurance Crater. Credit :NASA

However, to fulfill the overall Mars science strategy to “Follow the water”, the mobility of the twin robots was greatly enhance of its predecessor, Mars Pathfinder.

These newer robotic explorers have successfully trekked across the surface of Mars,

descended Martian crater and travelled uphill.

Figure 3. Spirit rover's Traverse map. Credit NASA

With total mileage of 11,671.23 meters (Opportunity, as of March 26, 2008) and 7,528 meters (Spirit, as of March 18, 2008) there is vast area that‟s still unexplored, or unable to be explored.

Figure 4. Martian surface from Mars Reconnaissance Orbiter. Credit :NASA

Figure 5. Ridge at Victoria crater, potentially fruitful targets for Mars Rovers. Credit :NASA

The rocker-bogies suspension system designed for both current Mars missions such as

the twin rovers, and future missions such as the Mars science lab, can withstand

ground tilt angle of 45 degrees with software limit of 30 degrees over relatively

benign terrain. These rovers were designed for long ranging, accurate and

uninterrupted autonomous traverse. But the remote sensing and remote imagery of the

surface of Mars suggest that water resources might be concentrated near cliff edges

outflows that will require aggressive mobility strategies to explore them in depth [20].

Figure 6. Show relative size between current and future Mars Rovers. Credit: NASA JPL

Figure 7. Actual Mars Science lab Rover. Credit:

NASA JPL

Furthermore, beside increase autonomy of operations and fault tolerance algorithm issues, the logical and desired evolution of exploration rovers would posses more all terrain capabilities. This will make it possible to explore numerous known and posited areas of the Mars surface that are not currently within safe reach of conventional rovers design yet promise to be high in science content [21]. Such regions are generally on extremely steep terrain, escarpments, fissures, breakout channels, cliffs, and steep crater walls, similar to searching for fossils on the Earth surface. The most interesting sites are traditional geological exposures such as cliff faces [22],[23].

Figure 8. Beagle2 Lander From ESA. Credit : ESA

Figure 9. Phoenix Lander from NASA. Credit :NASA

The late NASA and ESA Mars exploration missions concentrate on mobile science platforms and landers based science platforms to extract and analyze rock samples using limited onboard instrumentation.

Future missions will use lightweight, agile sample return rovers for “high risk access

and extreme maneuvers” to traverse highly variable, and rough terrain autonomously

[20] and return samples to Earth for in-depth analysis.

In this thesis work, we will present reconfigurable robot as the solution for the type of mission mentioned above.

1.2 Reconfigurable robots

Reconfigurable robots are robots that can reconfigure themselves physically, and adapt themselves in order to optimize the performance index, for example, speed, traction, stability, and power.

In some literatures, „reconfigurable‟ refers to the ability to change behavior of robots, but we do not regard this feature in this thesis.

Reconfigurable robots have flexible and adaptable characteristics, thus increasing the performance and survivability in a dynamic environment. Driving conditions can change dramatically over short distances, and might only be partially anticipated.

Thus reconfigurable robots are favorable for planetary surface exploration.

1.3 Thesis scope

The goal of this thesis work is to develop a small size reconfigurable robot, focusing on stability enhancement by use of active center of mass control, and conducting stability tests to compare the performance indices between conventional and reconfigurable systems where the index uses force-angle stability measure in quasi- static environment.

1.4 Thesis structure

Current mission and future trend are introduced and the reasons why reconfigurable

robots are interesting in the future have been introduced in Chapter 1. The next

chapter, Chapter 2, literature review, will begin with brief introduction of space

exploration history followed by examples of reconfigurable systems used in planetary

exploration missions and various types of stability measure have been studied and

commented on each measure. Chapter 3 will describe hardware design. Chapter 4 will

discuss software and control development. Tests and test results will show in Chapter

5. Chapter 6 will suggest the further work and the last chapter, Chapter 7, will be the

conclusions of this thesis work.

2 Chapter 2

Literature Review

In order to enhance the stability of the robots, we studied various types of stability measures. This literature review begins with brief history of space exploration and followed by examples of reconfigurable robots. Then, we give an overview on several stability measures originating mainly from the automotive industry, biped- locomotion/humanoid-robot researchers, and mobile manipulator researchers. There is no standard for general stability measurement. Thus, we analyze the existing measures with respect to their suitable work conditions and applications and draw conclusion after each measure.

2.1 Brief history of space exploration

The Moon, the Earth‟s closet neighboring planet and the only natural satellite, was first to be explored. The space race, the competition of space exploration between the Soviet Union and the United States during the years 1957-1975, effectively began after the Soviet launch of Sputnik 1 on 4

October 1957 and came to an end with joint Apollo-Soyuz mission in 1974.

Figure 10 The Moon. Credit: Lunar and planetary Institute

As the objective to land humans on the Moon, the American project Mercury and

Gemini provided the first experience of humans in space. They were precursors to the

Apollo program announced in 1961, which was accomplished in July 1969 by Neil

Armstrong- the first human to walk on the Moon‟s surface during the Apollo 11

mission. Five other Apollo missions also landed astronauts on the Moon until in year 1972, Apollo 17 mission, is marked as the last moon-walk mission and also the last manned mission beyond low earth orbit.

Figure 11. The first people on Moon in apollo11 mission.

Credit: NASA

Figure 12. Luna1 spacecraft. Credit : Alexander Chernov and the Visual Space Museum

On the other hand, the Soviet Union who has the enviable reputation of being “the first” in many aspects related to space flight, such as the success of placing the first satellite into orbit Sputnik1, the first animal (a dog) sent into Earth‟s orbit in Sputnik 2 and first animal (a turtle) to fly around the Moon in Zond 5, the first human in space, Yuri Gagarin in Vostok 1 and many other success. Soviet unmanned mission reached the Moon before the American Luna 1 in 1959 and successfully landed the first unmanned lunar rovers, Lunokhod 1, on the Moon in 1970 in the Luna 17 mission, Despite several unmanned sample return missions having been conducted, the Soviet union was unable to conduct manned flight to the Moon due to a lack of funding and personnel.

Figure 13. Lunokhod, Soviet Moon exploration Rover. Credit :Wikipedia

Figure 14. A photo from Lunokhod 1 showing the Luna 17 Lander. Credit :Wikipedia

Technologies, especially in space technology and human space flight have been

greatly developed during this race. The ability to explore the unknown planet either

by remote sensing, in-situ experiments and sample returns by manned missions and robotic space flights has enabled the key technology for exploring other planets beyond the Moon.

The next focus is to investigate the fundamental question, “are we alone?” The search for other life forms leads us to Mars, the most Earth-like planet in the solar system and, therefore, the only planet where life might have evolved.

Mars exploration has proven to be a far more sophisticated challenge than the Moon missions, shown by a high failure rate, about two-thirds of all spacecraft destined for Mars, due to complexity and a larger number of variables in interplanetary missions that might not have been taken into account during previous Moon missions.

Figure 15. Marsnik spacecraft. Credit: Wikipedia Figure 16. Rover that landed on Mars in 1971.

Credit :Wikipedia

The first Soviet attempt to gather data from the software of Mars was by Marsnik 1 in 1960. It was 11 years later, however, before the first successful Mars 2 mission in 1971 after 10 failed attempts.

The orbiter successfully managed to send data back confirming a “successful” crash landing on the surface of Mars, making it the first recorded object to touch down.

Only 10 days later, the Mars 3 mission was able to soft land but transmission ceased because of a huge dust storm on Mars. During this mission, the first Mars rover was on board, attached to the main Lander by 15 meter long tethers and moved by using a ski set on either side. These facts were not revealed for nearly 20 years after the mission. The Russian attempt to explore the surface of Mars ended in 1988 after 17 attempts without success.

Figure 17. Viking 1 orbiter. Credit :NASA Figure 18. Viking 1 Lander. Credit: NASA

On the American side, the Mariner 9 mission, used the same launch window of the Mars 2 and Mars 3 Russian missions, is the first successful orbit around Mars. After that, during the Viking 1 and Viking 2 first two Landers from America claimed the first successful touch downs in 1975. After these missions it was a further 21 years before the next landed mission and 25 years before the first attempted rover mission in year 1996, Mars Pathfinder lander/rover mission was successful by delivering the first Mars Rover (that functioned) named Sojonour, 6-wheeled vehicle with rocker-bogies suspension. It was 65cm long, 48cm wide, 30cm tall and weighed 10.6 kg as a technology demonstration of a way to deliver an instrumented lander and a free-ranging robotic rover to the surface of Mars, and the investigation from onboard scientific instruments on both the lander and rover suggest that Mars was at one time in its history warm and wet with water existing in its liquid state and a thicker atmospheric layer.

Figure 19. The first panoramic views by Viking 1 from the surface of Mars. Credit Wikipedia

Marked as the first space robotic exploration, an innovative method of directly entering the Martian atmosphere and landing using of large airbag to cushion the impact had been developed, as well as the novel rocker-bogies suspension having been tested. An algorithm used to control the rover that coped with inherent delay had also been utilized. This mission paved the way for the future of robotics exploration program.

2.2 Example of reconfigurable robots

A reconfigurable robots is defined as a robot that has an ability to adjust its structure configuration.

NASA/JPL has developed robots and group of robots that have the ability to reconfigure their structure and/or behavior to focus on the problem of “high risk access” to get an access to high-value high-risk planetary environment.

2.2.1 Sample Return Rover (SRR)

The concept of SRR, shown in Figure 20 and Figure 21, is to develop an advanced

science rovers, where adaptation and reconfiguration control based on on-board

sensor system facilitates access to challenging locations such as escarpments, fissures,

breakout channels, cliffs, etc. places which are considered to be geologically interesting for Mars exploration [16].

One of the work on this rover is work of K.Iagnemma [10], emphasis on improvement of the tip over stability margin by utilize two active shoulder joints of the robot and reposition its manipulator to redistribute the center of mass in order to maximize the pre-defined performance index(equation 2.1).

∅ = 𝐾

𝛾

+ 𝐾

𝜃

− 𝜃

𝑛 𝑖=1

(2.1)

Where 𝛾

Is stability angle determined by the force-angle stability measure (discussed in 2.2.3 Force-Angle base stability margin), 𝜃

are nominal values of the i

joint variables and K

are constant weighting factors.

Figure 20. Jet propulsion laboratory Sample Return Rover [10]

Figure 21. Jet propulsion laboratory Sample Return Rover [10]

The experiment result is very interesting. After conduct the experiment in the Mars-

like terrain (Arroyo Seco in Altadena, California) that threatened the rover stability,

stability index of the case when joints are fixed and with reconfigurability algorithm

activated are compared.

Figure 22. SRR stability margin for reconfigurable system (solid) and non-reconfigurable system (dashed)

It shows that stability margin improved 48% over the fixed joint case. Clearly kinematic reconfigurability results an improved stability on rough terrain.

2.1.2 Reconfigurable wheel

A.Siddiqi studies the use of a reconfigurable wheel on planetary surface vehicles (PSVs), [16], to travel over various terrain conditions that might change dramatically even within small radius of exploration or in partially unknown terrain, and this may trap the rover like in the case of Mars Exploration Rovers (MER) in year 2005. The rover was immobilized over the course of its explorations due to an unanticipated change in soil condition [16].

Figure 23. One of the wheels of MER (opportunity) stuck in sand on Mars. (NASA)

The reconfigurable wheel is a conceptual design wheel that can vary the diameter, Figure 24. Wheel diameter is directly related to torque and power consumption of the vehicle, for example in relatively flat terrain the wheel can be retracted to conserve energy or can be adjusted to the suitable diameter for each terrain environment depend on how much torque/velocity is needed. The work of A.Siddiqi also studies the algorithm to determine when the wheels should adjust its diameter to maximize the vehicle performance.

Figure 24 Reconfigurable wheel with variable diameter concept by brian Izard. (Michelin)

2.3 Type of stability margin

2.2.1 Center of gravity and zero-moment point based stability margin

R.B. McGhee and A.A. Frank developed a margin based on center of gravity and zero-moment point in “on the stability of quadruped creeping gait” [1] in 1968. They developed a series of definitions and theorems concerning the static stability of legged machines.

The magnitude of the static stability margin for an arbitrary support pattern is equal to the shortest distance from the vertical projection of the center of gravity to any point on the boundary of the support pattern. If the pattern is statically stable, the stability margin is positive, otherwise it is negative. R.B.

McGhee and A.A. Frank

The margin concern only the static case and is only approximate for systems on uneven terrain and insensitive of top heaviness.

Later on after M. Vukobratovic and D. Juricic implicitly introduce the concept of

ZMP in “Contribution to the synthesis of biped gait” [2] in 1968 and explicitly

introduced it later on in year 1970. Its first practical demonstration took place in

Japan in 1984 at Waseda University in the first dynamically balanced robot WL-

10RD of the robotic family WABOT. Since then, the ZMP have been widely used in

biped locomotion and humanoid robot researchers to analyze the stability of the

robots and to determine the footing position to maintain stability in dynamic walking mode.

Figure 25. WL-10RD first dynamic walk robot[13] Figure 26. Planned trajectory for a walk on spiral stair[14]

S.Sugano and colleagues extend the work of McGhee by the ZMP approach to include dynamic movement of mobile manipulator. The goal of this work is to keep mobile manipulator in a stable region while executing a given task.

2.3.1.1 Zero-moment point

Zero-moment point is defined as “a point on the floor where the resultant moment of the gravity, the inertial force is zero”

Figure 27. Definition of Vectors for Mobile Manipulator [3]

By applying D‟Alambert‟s Principle [12] the ZMP point can be derived as follows

𝑥

= 𝑚

𝑧 + 𝑔

𝑥

− 𝑚

𝑥 + 𝑔

𝑧

+ 𝑀

+ (𝑆

𝐹

− 𝑆

𝐹

)

𝑚

𝑧

+ 𝑔

− 𝐹

(2.2) 𝑦

= 𝑚

𝑧 + 𝑔

𝑦

− 𝑚

𝑦 + 𝑔

𝑧

+ 𝑀

+ (𝑆

𝐹

− 𝑆

𝐹

)

𝑚

𝑧

+ 𝑔

− 𝐹

(2.3)

Where; 𝑚

: mass of particle i

𝑟

= [𝑥

𝑦

, 𝑧

]: position vector of particle i

P = [𝑥

𝑦

, 0]: position vector of point P G = [𝑔

𝑔

, 𝑔

]: gravitational acceleration

T = [𝑇

𝑇

, 𝑇

]: resultant torque acted on point P 𝑀

= [𝑀

, 𝑀

𝑀

]: external moment j

𝐹

= [𝐹

, 𝐹

, 𝐹

]: external force k

𝑆

= [𝑥

𝑦

, 𝑧

]: position vector of external force k

For more in-depth notion of the ZMP one may consider “Zero-Moment point – Thirty years of its life” [24] from M.Vukobratovic the inventor of the method himself, he state that the objective of the literature is to “refreshing the ZMP notion and re- stressing its basic meaning”. On the other hand, A.Goswami also try to restate the use of ZMP in his work, “foot-rotation indicator (FRI) point”[25] , which state the problem of improper use and loose definition of ZMP in various literature and thus introduce the FRI point to correct the problem but there are some conflict between his work and M.Vukobratovic [24] in the subject of whether or not center of pressure (CoP) are the same of ZMP or not.

2.3.1.2 Stability Degree and Stability Region

Stability criterion: “if the ZMP is inside the support polygon (stable region) the mobile manipulator is stable” [3]

To quantify the stability according to the relationship between the ZMP position and the stable region defined in the stability criterion the stability degree is defined as

𝛼 = 𝑑 𝑟

(2.4)

𝑑 = min⁡[𝑑(𝑍𝑀𝑃)] (2.5)

𝑟

= max⁡[𝑑: 𝑑 ∈ 𝐴 𝑑 ] (2.6)

The stability degree 𝛼 is positive (between 0 to 1) if the system is stable and

negative if the system is unstable. 𝑑(𝑍𝑀𝑃) Is a set of the distance from ZMP

to the boundary of the stable region d is the minimal distance from ZMP to the

boundary of the stable region (Figure 28). [3]

Figure 28. Valid Stable Region and Stable region[15]

Figure 29. Stable Region and Stability Degree [4]

2.3.1.3 Criteria of stability evaluation

To make sure that the mobile manipulator will stay stable while performing task and/or being disturbed by external force, valid stable region (Figure 28) is defined as the stable region which the stability degree will not become negative under the toleration disturbance, this measure is then can be said to considering the known influence of the environmental disturbance in which no former measure (center of gravity based measure) does, in the case of the ZMP being inside the valid stable region, the mobile manipulator is still stable even if it is disturbed by the toleration disturbance. Thus no need of concern about its stability while performing the task. In case of the ZMP being outside the valid stable region and inside the stable region, the mobile manipulator will become unstable if it is influenced by the toleration disturbance. Therefore, it is necessary for the mobile manipulator to be controlled for its stability and its task at the same time. And in the case of the ZMP being outside the stable region, the mobile manipulator is unstable. In such a case it is necessary that the mobile manipulator be controlled only for its stability.

2.3.1.4 Stability control system

According to the criteria of stability evaluation it is necessary to maintain ZMP inside the valid stable region in order to maintain the stability while performing the given task, in case of ZMP go out of the valid stable region or stable region it is then desirable to bring it back in to the valid stable region, the method of ZMP path planning by using potential field have been developed by S.Sugano “Stability Control for a Mobile Manipulator using a Potential Method”[4] principle of the method is to assign high potential at the edge of the stable region and lower at the middle of the field which have largest stability degree, and also define as “goal state” in this paper, the potential function consist of two part, ∅

and ∅

,can be describe as follow,

∅ = ∅

𝐷

+ ∅

(𝐷

) (2.7)

∅

= − 𝐾

𝐷

(2.8)

∅

= 𝐾

𝐷

+ 𝐷

(2.9)

Where ∅ is a stability potential function, ∅

is a function with respect to the center of the stable region and the center of the stable region is regarded as the goal state of the stability. ∅

is a function with respect to the boundary of the stable region, where 𝐷

is the distance between boundary of stable region and prohibitive state, 𝐷

is the distance from the ZMP to the center of the stable region, 𝐷

is the minimum distance from the ZMP to the boundary of the stable region (Figure 30)𝐾

, 𝐾

are coefficients for adjusting the potential proportion of the goal state and the prohibitive state of stability.

Figure 30. Concept of the goal state and the prohibitive state of stability [4]

The ZMP govern by this function is then tend to move in to the middle of the stable region and try to balance the distance from each stable region boundary , which yield in increasing of stability degree to maximum.

ZMP path can be derived by iterate following equation,

𝑃(𝑛 + 1)

= 𝑃(𝑛)

− ∆𝑆 × 𝑔𝑟𝑎𝑑∅

𝑔𝑟𝑎𝑑∅ (2.10)

Where, ∆𝑆 is the changed amount of the ZP position, 𝑔𝑟𝑎𝑑∅ is the gradient of the potential function.

Figure 31 Potential field and ZMP path [4]

An example of ZMP path shown in Figure 31, while curve (1) is the ZMP path which only consider the center of the stable region, curve (3) is the one which only consider the boundary of the stable region, and curve (2) is the one by stability potential field considering balance of the center and the boundary of the stable region.

2.3.1.5 Conclusion on Center of gravity and Zero-moment point based stability margin

The major drawback of center of gravity based margin is it‟s not support dynamic case while ZMP base margin can support both static and dynamic cases.

ZMP base stability margin have been widely use in legged locomotion and mobile manipulator since the first introduction of ZMP principle and working well on flat and planar surface, and by keeping the ZMP in the center of support polygon make it intuitively correct and easy to compute, in next section (2.2.2 energy base stability margin) this measure will proved to be not accurate on inclined or rough terrain case, which is likely to be the case for outdoor robots, even though the work of S.Sugano is an extent of work from McGhee this measure have been improved by include dynamic movement of the mobile manipulator but still remain insensitive of top heaviness and according to [5] the work from McGhee have been extended further by several researcher, Sreenivasan and Wilcox improve on the minimum distance measure by considering the minimum of each contact point distance to the net force vector eliminating the need for a projection plane and thereby making the measure exact [6]. Davidson and Schweitzer also extend the work of McGhee by using screw mechanics thus eliminates the need for a projection plane while allowing for angular loads [7]. However both of the extended work [6], [7] and work of S.Sugano presented above is not sensitive to top heaviness.

Notice that there are slight abuses of the use of ZMP in this topic because by definition ZMP can only exist inside support polygon and can only stay at the edge of the support polygon in case of tip-over or losing stability. ZMP positioned outside the support boundary is named fictitious zero moment point (FZMP) according to notion of M.Vukobratovic [24] but the equation to locate either FZMP or ZMP are the same.

2.3.2 Energy based stability margin

Before explanation of energy based stability margin it is better to state the fault of ZMP base approach according to work published by Messuri and Klein [8] as followed.

“Consider, as an example, the situation depicted in Figure 32. The vehicle

has four supporting legs and is standing on an inclined plane, with the body

horizontal. According to the previous definition Criteria of stability evaluation mentioned above, the support pattern, in this case, is a rectangle formed by the vertical projection of the four supporting feet onto the horizontal plane.

Assuming that the center of gravity of the vehicle is located at the center of the vehicle body, then the position shown represents the maximum static stability margin for this type of situation since the vertical projection of the center of gravity will be at the center of the rectangular support pattern. However, intuition seems to indicate that the vehicle is more likely to tip “down-hill”

rather than “up-hill” This suggests that maximum static stability would be achieved for the given situation if the body were shifted some distance in the uphill direction, to the point where there would be an equal likelihood of a downward tip or an upward tip.” Messuri and Klein [8]

This observation leads to the realization that the ZMP based margin does not provide a sufficient measure for the amount of stability when the terrain is not a horizontal plane.

Figure 32. Vehicle standing on an inclined plane with the body horizontal. [8]

Messuri and Klein propose the use of minimum work required to bring the center of gravity point on to the edge of support polygon and thus bring the vehicle to tip over state as the energy stability level.

“Definition: The energy stability level associated with a particular edge of a support boundary is equal to the work required to rotate the body center of gravity, about that edge, to the position where the vertical projection of the body center of gravity lies along that edge of that support boundary” [8]

For example, consider Figure 33, The change in vertical height though which the body center of gravity is moved from its original position to this position of zero static stability margins is given by the distance 𝑕

for rotate about the rear edge and

𝑕

about the front edge , Since 𝑕

= 𝑕

+ ∆𝑕 the situation in Figure 33 require less

energy to overturn the vehicle about the rear support as opposed to the front support

legs. Therefore, if it were desired to shift the body to a position of greater overall

stability, the body should be shifted such that 𝑕

equal 𝑕

, at which point the energy

stability levels for the front edge and rear edge would be equal.

Figure 33. Side view showing a geometrical comparison of the energy stability Level for the front and rear edge of the support boundary [8]

For this relatively simple case we can describe locus of all points representing the location of the body center of gravity with 𝑕

equal to 𝑕

by hyperbola curve with has focal point at 𝐹

and 𝐹

which shown by dash line in Figure 33 and Q point is the suitable point on the hyperbola for move center of gravity into because the minimum height and intersection with center of gravity moveable path.

But for general situation, especially in the case of very rough terrain, may not permit a simple geometric solution, therefore, a general equation is necessary. By using potential energy equation given by,

𝑃𝐸 = 𝑚𝑔𝑕 (2.11)

Where 𝑚 is mass and 𝑔 is gravitational acceleration, then the only variable for finding the energy stability is height, 𝑕 .

Figure 34 Derivation of the energy stability level equation [8]

Consider the general situation depicted in Figure 34, where points 𝐹

and 𝐹

represent the contact points with ground and line 𝐹

𝐹

connecting 𝐹

and 𝐹

is

represent one edge of the support boundary,plan1 is the vertical plan contain these

two point, COG point represent the center of gravity point vector 𝑅 is a orthogonal

vector from line 𝐹

𝐹

to COG point, angle 𝜃 is the angle between COG and plane1 and angle Ψ is the angle between 𝑅 and vertical direction vector 𝑧 , 𝑕 is then given by,

𝑕 = 𝑅 (1 − 𝑐𝑜𝑠𝜃)𝑐𝑜𝑠Ψ (2.12)

By considering the energy stability margin as a function of the position of the projection of the center of gravity in the present plane of the body, one can draw the optimal path of the vehicle is center of gravity, which are the locus of all point, in the present plane of the body to which the body center of gravity could be moved and still maintain a given energy stability margin.

Figure 35. Optimal path of the vehicle center of gravity for various vehicle configurations [8]

Later on, A.Ghasempoor and N.Sepehri [9] extend the work of Messuri and Klein by

adding destabilizing force and moments other than gravity, by distinguish total force

act on the vehicle into two category, conservative force and non-conservative force

and moments. Therefore, instead of only vertical plane, equilibrium plane have been

added to describe the energy stability calculation.

Figure 36. Stability level calculation [9]

Figure 37. Machine and gravity coordinate system [9]

2.3.2.1 Equilibrium plane [9]

Equilibrium plane describe as a plane inclined angle of ∅ from the vertical plane. In this plane the sum of all the forces and moments equals to zero.

𝐹 ∙ 𝑡 𝑅 + 𝑀 ∙ 𝑏 + 𝑚𝑔 𝑄 𝑐𝑜𝑠𝛼 𝑠𝑖𝑛∅ = 0 (2.13)

2.3.2.2 Work calculation for conservative forces [9]

The only conservative forces in this system is weight, the work require for rotating the center of gravity around support boundary to the equilibrium plane depend only on vertical displacement of center of gravity denoted by 𝑕 (see Figure 37),

𝑊

= 𝑚𝑔 𝑄 (𝑐𝑜𝑠∅ − 𝑐𝑜𝑠𝜓)𝑐𝑜𝑠𝛼 (2.14) Where 𝜓 is the angle between 𝑄 , the orthogonal vector from line 𝑓

𝑓

to CG point, and 𝑠 , a vector perpendicular to 𝑓

𝑓

in vertical plane, angle 𝛼 represent the angle that support boundary edge 𝑓

𝑓

make with horizontal plane .

2.3.2.3 Work calculation for non-conservative forces [9]

Non-conservative forces are destabilizing force and moments other than gravity force and assumed to be constant over all duration of turn over about support boundary.

𝑊

= 𝐹 ∙ 𝑡 𝑅 + (𝑀 ∙ 𝑏 ) 𝜃 (2.15)

Where; 𝜃 = 𝜓 + ∅ .

2.3.2.4 Total energy stability level [9]

Energy stability for each edge is then equal to difference between conservative and non-conservative force.

𝐸𝑛𝑒𝑟𝑔𝑦 𝑆𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝐿𝑒𝑣𝑒𝑙 = (𝑊

− 𝑊

) (2.16)

Notice that for finding energy stability margin, energy stability level of each support boundary edge has to be calculated and the minimum of all energy stability level is then called energy stability margin.

2.3.2.5 Effect of top heaviness [9]

The work of A.Ghasempoor and N.Sepehri[9] also demonstrates the unique capability of energy based measure over ZMP based measure, by show the difference in energy stability margin between two poses of mobile manipulator, effect of top heaviness.

Configuration 1 caused the center of gravity to shift 72cm vertically relative to configuration 2 and this increased the top-heaviness. The margins of energy stability for configuration 1 was therefore lower (see Figure 39). This reduction of margin of stability caused by increased top-heaviness cannot be shown by ZMP based method.

2.3.2.6 Conclusion on energy based stability margin

Even though the energy based stability margin have more complication than ZMP based method , it have been proved to support more general cases including the case of inclined slope and rough terrain and effect of top heaviness show the importance of position of center of gravity of the vehicle which will not affect the stability margin in ZMP based method.

Figure 38. Configuration1 and 2 [9] Figure 39. Effect of top-heaviness. [9]

2.3.3 Force-angle Based Stability Measure

E.G.Papadopoulos and D.A.Rey propose Force-angle stability measure in “A New Measure of Tip over Stability Margin for Mobile Manipulator”[5] .Using geometric method thus more easily computed (than work of A.Ghasempoor and N.Seppheri, energy based stability measure mentioned above), sensitive to top-heaviness and support general cases of rough terrain.

As the name of the measure suggest, Force-angle Based Stability Measure relies on the angle between total force acting on center of gravity and candidate tip-over axis normal, this way the effect of top heaviness can be easily visualized as shown in Figure 40and Figure 41respectively.

For example, in case of Figure 40, Force vector subtends two angle, 𝜃

and 𝜃

with the two tip-over axis normal 𝑙

and 𝑙

.The force-angle stability measure, 𝛼 ,is given by the minimum of the two angle, 𝜃

in this case, weighted by the magnitude of the force vector for heaviness sensitivity.

𝛼 = 𝜃

∙ f

(2.17)

The magnitude of a positive 𝛼 describes magnitude of the tip-over stability margin of a stable system. Critical tip-over stability occurs when 𝛼 = 0. Negative values of 𝛼 indicate that a tip-over instability is in progress.

Figure 41illustrate the case where center of gravity has been raised, clearly results in a minimum angle and a reduced measure of tip-over stability margin.

Based on method to determine the force-angle stability measure above, in more general case we define support polygon, where contact point with the ground form a convex support when projected onto the horizontal plane.

Figure 40. Planar Force-angle stability measure [5]

Figure 41. Effect of center-of mass height (top- heaviness) [5]

Figure 42. Support polygon [5]

Where 𝑝

represent the location of the 𝑖

ground contact point, numbered according to right hand rule, and 𝑝

represent the location of the vehicle center of mass, line which join point of contact 𝑝

are the candidate tip-over axis𝑎

, and set of these line will be referred to as the support pattern. The 𝑖

tip-over axis is given by.

𝑎

= 𝑝

− 𝑝

, 𝑖 = 1, … . , 𝑛 − 1 (2.18) The net force acting on the center of gravity point would participate in a tip-over instability,𝑓

is thus given by,

𝑓

= (𝑓

+ 𝑓

+ 𝑓

− 𝑓

) (2.19) Similarly, for the net moment 𝑛

acting about the center of gravity.

𝑛

= (𝑛

+ 𝑛

+ 𝑛

− 𝑛

) (2.20) Only those components of 𝑓

and 𝑛

which acts about the tip-over are considered, so we let

𝑓

= 1 − 𝑎

𝑎

𝑓

(2.21) And

𝑛

= 𝑎

𝑎

𝑛

(2.22)

Since the force-angle stability measure is based on the computation of the angle between the net force vector and each of the tip-over axis normal, it is necessary to replace the net moment 𝑛

with an equivalent force couple, f

, for each tip over axis.

f

= l

× n

l

(2.23)

Where, l = l/ l , then the new net force vector, 𝑓

, for the 𝑖

tipover axis is thus

𝑓

= 𝑓

+ l

× n

l

(2.24)

Letting 𝑓

= 𝑓

/ 𝑓

, The force -angle stability measure are then simply given by

𝜃

= 𝜎

𝑐𝑜𝑠

𝑓

∙ 𝑙

, 𝑖 = 1, … . , 𝑛 − 1 (2.25) The sign of 𝜃

is determined by 𝜎

as follows

𝜎

= +1 , l

× 𝑓

∙ 𝑎

< 0

−1, 𝑜𝑡𝑕𝑒𝑟𝑤𝑖𝑠𝑒 (2.26) The overall Force-angle stability measure is then simply given by

𝛼 = min⁡(𝜃

) 𝑓

, 𝑖 = 1, … . , 𝑛 − 1 (2.27)

2.3.3.1 Conclusion of Force-Angle based Stability Measure

Unlike ZMP and energy based method that implemented only by computer

simulation, Force-angle based stability measure have been implemented by various

work of K.Iagnemma et.al in real application, proved to work in very rough

terrain[10] and correctly predict the tip-over event on high speed vehicle[11] this

method is then will be pursued on this research project.

3 Chapter3

Hardware Design and Development

This chapter will describe component developed for the robot, the chapter will separated into two main part, Mechanical design and Electronics design.

3.1 Mechanical Design

Since the objective of this thesis work is to develop the robot with reconfigurable ability in order to adapt itself in the way that improve its stability index. Since the only reconfigurable robot available at TKK automation laboratory is work partner robot since it is occupied by several research teams and it‟s already posses “the traditional way” to enhances the stability, the new, affordable, reconfigurable robot have to be designed and developed.

In designing phase, the rough criteria are defined as followed.

 The robot has to be small and has a movable mass to shift center of mass of the robot.

 The manipulator design must be easy to develop and don‟t obscure the mobility of the robot.

The robots are first visualize by the use of CAD/CAM design program, CatiaV5, and approved by the instructor before moving on to implementation phase, shown below is three models from preliminary design phase.

Figure 43 Rack and pinion configuration

Figure 44 Belt and pulley configuration

Figure 45 Inverted pendulum configuration

Later on, the Inverted pendulum configuration, Figure 45, has been selected by consideration of manipulator size and ease of implementation. The designed is then refined several times to ensure the functionality of the robot and update the actual design to match with planed design or vice-versa.

Figure 46 The very first impression

Figure 47 1st refined design

Figure 48 Take material strength and functionality

into account

Figure 49 Improved structure and include circuit

mass

With aid of the 3D Mechanical design, drawing of each element in the robot have been updated regularly because dimension and weight of each component, which may deviated from actual design due to available parts and tools, will reflect on mass and size of the overall system which will be the important information in finding the location of center of mass, the parameter element in order to develop this thesis work.

Figure 50 Example on finding COG in each part

Catia V5 offer the function to locate center of mass of the robot, base on user defined

density and volume of each element, the accuracy is depend highly on how accurate

user input are, in this project each and every component have been added into account

with actual mass and volume to ensure that the calculated center of mass is as precise

as possible, the output is therefore reasonably accurate as will be describe later in

chapter 4, test and test result chapter. The robot best describe separately in to two

main part, mobile platform and inverted pendulum.

Figure 51. Final designed version in CAD and actual hardware

3.1.1 Mobile platform

Figure 52. Mobile platform

As the name suggest, mobile platform give the robot‟s ability to move, with leg-

wheeled configuration to increase ground clearance, the importance aspect for

outdoor vehicle and thus jeopardize the platform‟s stability if not managed well, and

large aluminum plate on top to place electronic component and actuator. The wheel

drives by two geared DC motor able to achieve maximum speed of 30cm/sec but

limited by software to approximately 10cm/sec.

3.1.2 Inverted pendulum

Figure 53. Inverted pendulum

Inverted pendulum, or motorized inverted pendulum to be more exact, at the tip of the pendulum is high torque motor, rated 3Nm weight 1kg, powerful enough to lift itself from 90 degree position from 354mm long pendulum rod, used as the source of reconfiguration by shifting the center of mass of the whole system. At its base is right angled aluminum gear box convert the movement of the motor shaft around horizontal axis of the robot to vertical axis, enable the pendulum to turn full 360°

degree around the axis, the movable path of the pendulum is then upper half sphere with radius of 354mm, with use of worm gear, reduction ratio is at 30:1 from DC geared motor make it over 5700:1 reduction ratio in total, make it very slow, the maximum speed at the output shaft is 1 round/minute.

In summary, as shown in Figure 51, the final version of the robot intend to have high center of mass in order to emphasis on improvement of stability, the robot has skid- steer platform driven by DC motor with belt and pulley mechanism. On top of it is turn table part, consist of set of worm gear in aluminum box to support pendulum part, give robot the ability to rotate the pendulum around vertical axis. In pendulum part consist of high torque DC motor on top and connected with pendulum‟s base via belt make it able to move pendulum in -90° to 90° range about horizontal axis.

With these configuration it‟s similar to sample return robot(SRR), developed by

NASA and have been modified to study the reconfigurability method for stability

enhancement[10], without two shoulders actuator that make the SRR able to adjust its

height and developed robot has a much heavier inverted pendulum like manipulator

instead of composite light weight robot arm on SRR‟s, this will be a good comparison

between two ways of redistribute the center of mass, one put more weight on

adjusting the shoulder angle(the traditional way) and other is emphasis on moving the mobile mass.

3.2 Electronics Design

The electronics part divided into three main component, microcontroller, sensor and motor driver part.

Figure 54 Show actual circuit boards

3.2.1 Microcontroller

Microcontroller part consist of two crumb128-CAN board, Rapid prototype module with AT90CAN128 microcontroller from chip45.com, equipped with all necessary peripherals, for example, USB device interface, standard serial port with RS232 transceiver, on chip 10-bit ADC , to facilitate and expedite time for develop a new hardware.

Figure 55 Crumb128-CAN Board. Credit : Chip45.com

Each crumb board primarily run PID control loop for one DC motor with quadrature

encoder (turn table motor/pendulum motor) in position control mode, one controller

board control only one motor because the limited number of register available on each

microcontroller, and more importantly, to keep track of encoder count and keep up an

moderate control update rate, 28 time/sec, and also run others minor task such as read sensor data, communicate with MATLAB and take control command from joystick.

The developed circuit for the two controller board have minor different due to task distributions, simplified circuit diagrams of the two circuits shown in Figure 56 and Figure 57.

Crump 128-CAN (Turntable)

ADC1 Serial0 Serial1

ADC2

Motor DIR

PWM Dir ENA

SCA610 1axis Accelerometer/

Inclinometer

SCA610 1axis Accelerometer/

Inclinometer

LS7184 Quadrature clock

converter

Ch.A

Ch.A Ch.B

Ch.A Ch.B I

Quadrature encoder (Turntable)

Dir

L9904 Motor Driver

Board (Turntable)

Crump 128-CAN

(Pendulum) MATLAB

Figure 56 Circuit Diagram on Turntable part

Crump 128-CAN (Pendulum)

ADC1 Serial0

Motor DIR

PWM Dir ENA

SCA610 1axis Accelerometer/

Inclinometer

LS7184 Quadrature clock

converter

Ch.A

Ch.A Ch.B

Ch.A Ch.B I

Quadrature encoder (Pendulum)

Dir

L9904 Motor Driver

Board (Pendulum)

Crump 128-CAN (Turntable)

PWM Dir ENA PWM Dir ENA

L9904 Motor Driver

Board (Right) L9904 Motor Driver

Board (Left)

Joystick

Figure 57 Circuit Diagram on Pendulum Part

3.2.2 Sensor

The robots have 3 one axis accelerometers/inclinometer, SCA610 Series from VTI technologies, to measure state of the robot, one of the sensors is used to measure tilt angle of the pendulum, even though the angle can calculated from pulses sensed from encoder, which is relative measurement sensor the accelerometer is then needed to make absolute measurement at base position.

The other two accelerometers are used to measure the tilted angle of the robot with respect to ground, the important information to calculate the force-angle stability.

Outputs of these sensors are in analog value with zero point, sensor plane perpendicular to the gravity vector, is at 2.5volt. The sensor output is 0 to 5 volt at -90° (-1g) and 90° (1g) respectively. Unfortunately, the output is linear only between

±0.5g, with no further information from the devices datasheet [18] simple experiment

is conducted to find the right conversion equation between output voltage and angle.

The test is straight forward; the sensor is mouthed on incline plane with known angle and then collects the data to plot output voltage with respect to tilted angle, every 10°

degree, the test result shown in graph below.

Figure 58 Accelerometer output with least square error equation

The data is fitted with least square error method, the graph, as suggested from its datasheet [18], is linear only between 50° to -50° degree. So the equation is divided into 3 separate equations to achieve less deviation than considering one equation that governs the whole range of data.

y = -0.218x + 110.1 R² = 0.997

y = -0.680x + 241.9 R² = 0.897

y = -0.615x + 398.1 R² = 0.916 -100

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850

Tilied Angle

Analog output

50 to -50 90 -90

3.2.3 Motor Driver

The robot has four motors driver circuit for each motor on the robot. L9904 motor bridge controller chip used to control 4 Metal Oxide Semiconductor Field Effect Transistors (MOSFETs) in H-bridge configuration according to three input command sequence, enable, direction and pulse width modulation (PWM).The PWM signal generated by microcontroller in 10bit fast PWM mode at 16kHz. Since it use direction and speed control scheme the software have to make sure that the motor will not suddenly turn to opposite direction while the motor still running which may cause circuit break down.

Figure 59 Drive sequence of L9904 motor bridge controller chip. Credit :STMicroelectronics

Figure 60 Connection between the chip and MOSFETs. Credit :STMicroelectronics

4 Chapter4

Software and Control

The low level control loop runs on the robot‟s microcontroller, written in C language, will control the position of the actuator and read and send sensor, motor encoder data, as requested from the higher level control loop which implemented on MATLAB, where calculation and optimization of force-angle bases stability measure are done, Actuator of the robot is then controlled automatically by high level control from MATLAB but the mobility of the robot is controlled independently by joystick.

Software and control part has two separated part, Microcontroller part, where low level control are implemented, and MATLAB part, where the theory of force-angle stability measure and high level control have been implemented.

4.1 Microcontroller

As state earlier, two microcontrollers have been used on this robot. To communicate

with both microcontrollers we connect it together with serial communication thus

only one microcontroller will communicate with MATLAB, the microcontroller

board that control turntable part is act as master controller and the other one that

control pendulum motor is slave. Every command from MATLAB will go through

only master controller and then the master microcontroller will convey the command

to slave, only if necessary, via serial communication and data transmit from slave

controller will then have to transmit to master controller first. The flow chart of the

two microcontrollers is then difference due to this master-slave configuration and also

from hardware connection. The flow charts shown in Figure 61 and Figure 62.

Timer 0 overflow?

Read position

Calculate Velocity

Calculate Error

Motor driver Trajectory ,PI control

Control command

request

Send command to other microcontroller

Which Micro controller

Execute command

Motor1 Joystick control

Motor2 Motor3 Motor4

End Yes

No

Yes

Yes

No

No

Pendulum Turntable

Start

Figure 61 Flow chart of master controller

Timer 0 overflow?

Read position

Calculate Velocity

Calculate Error

Motor driver Trajectory ,PI control

Control command

request

Execute command

End Yes

No

Yes

No Start

Figure 62 Flow chart of slave controller

In addition of trajectory control mentioned in both flow charts, it is the mean of position control scheme which is difference between the two motor, turntable and pendulum.

The motor at the turntable is already very slow and thus able to stop immediately

when command issued. So the position control algorithm is then straight forward by

using PI control with maximum speed of the motor, the speed is not controlled at all

only position is concerned.