DESIGN AND CONTROL OF AUTONOMOUS MOBILE ROBOTS WITH IMPROVED DYNAMIC STABILITY 1

1.3 Single Wheel Robot1.3.1 Introduction Gyrover is a single-wheeled gyroscopically-stabilized mobile robot developed at CarnegieMellon University [14]-[15].. For stabilization problem o

Chapter 1

Background and Literature Review

Perspec-tive

Most mobile machines and, particularly mobile robots, roll on wheels [1] Althoughlegged and treaded locomotion were intensively studied and corresponding mobilerobots were developed in the last decade, it is commonly accepted that “wheeledmobile robots are more energy-efficient than legged or treaded robots on hard, smoothsurface”[2] Wheeled robots are mechanically simple and easy to construct “Wheelsare simpler to control, pose fewer stability problems, use less energy per unit distance

of motion, and can go faster than legs”[3]

A definition of Wheeled Mobile Robot(WMR) found in [2] states: “A robot

ca-pable of locomotion on a surface solely through the actuation of wheel assembliesmounted on the robot and in contact with the surface A wheel assembly is a devicewhich provides or allows relative motion between its mount and a surface on which

it is intended to have a single point of rolling contact”

WMR is classified according to the wheel arrangements as follows [1]:

• Differential Drive;

• Synchro Drive;

• Tricycle Drive Robot;

• Car-like Drive Robot;

A review and classifications of WMR with the aforementioned wheels were ported in [2] WMR with conventional and omni-directional wheel were analyzed in[4] In [5], the unified kinematics, both inverse and direct, is derived for four kinds ofwheeled vehicles: ordinary car-like robots (including passenger cars, single unit trucks,single unit buses, and articulated trucks); dual drive robots (dual drive motors withvarious casters); synchronous drive and steering robots; and omni-directional robots.Rajagopalan [6] analyzed the kinematics of WMR with various combinations of-driving and steering wheels It was shown that for driverless ground vehicles (WMRs)

re-operating at low speed (<10 km/h) and not undergoing frequent accelerations and

de-celerations, the ”frictional effects are insignificant” and a kinematic model is sufficient

On the other hand, Shekhar [7] proved that for fixed, centred, and omnidirectionalwheels, wheel slip is inevitable, for they cannot preserve the longitudinal (rollingdirection) constraints

The most recent overview analysis of the development and classification of ferent kinds of wheeled mobile robots can be found in [1]

dif-For all these kinds of mobile robots, the nonholonomic constraints reduce therange of different motions allowed, thereby greatly complicating the motion planningproblem In approaching this problem, different mechanisms for omni-directionalwheels have been developed in the past decades, namely, offset steered driving wheels;omnidirectional wheels; spherical wheels: orthogonal-wheel assembly mechanisms;spherical robots; ball-wheel omnidirectional mechanisms; etc Vehicles with omnidi-rectional wheels can freely move back, forth, and sideways or rotate in place.

Luca [8] and Murry [9] stated that nonholonomy usually rises from three differentsources:

1 Rolling Contacts without slip;

2 Conservation of angular Momentum in multibody systems;

3 Robotic devices under special control operation;

In the first case, typical applications are:

• Wheeled Mobile robots and vehicles, where the rolling contact takes place

be-tween the wheels and the ground

• Dexterous manipulation with multifingered robot hands, with the constraint

arising from the rolling contact of fingertips with the objects

The second situation in which nonholonomic constraints come into play when body systems are allowed to float freely, i.e., without having a fixed based The

multi-conservation of angular momentum yields then a differential constraint that is notintegrable in general Systems that fall into this class are:

• Robotic manipulators mounted on space structures.

• Dynamically balanced hopping robots in the flying phase, mimicking the

ma-neuvers of gymnasts or divers

• Satellites with reaction (or momentum) wheel for attitude stabilization.

In these cases, the term used for the constraint is “differential” in place of matic” for the constraints, because conservation laws depend on the generalized in-ertia matrix of the system, and thus contain also dynamical parameters

“kine-One more source of nonholonomic behavior is the particular control operationadopted in some robotic structures Some examples are:

• Redundant robots under a particular inverse kinematics control.

• Underwater robotics systems where forward propulsion is allowed only in the

pointing direction

• Satellites with reaction (or momentum) wheel for attitude stabilization.Robotic

manipulators with one or more passive joints

The nonholonomic behavior is a consequence of the available control capability

or chosen actuation strategy In fact, all these examples fall into the category ofunderactuated systems, with less control inputs than generalized coordinates It also

worth noting that in the last kind of system the nonholonomic constraint is alwaysexpressed at the acceleration level.

Nonholonomic constraints arise in many advanced robotic structures, such as mobilerobots, space manipulators, and multifingered robot hands Nonholonomic behaviorcan be completely controlled with a reduced number of actuators, because it impliesthat the mechanism can be completely controlled with a reduced number of actua-tors On the other hand, both planning and control are much more difficult than inconventional holonomic system and require special techniques

This section provides a brief overview of the general area of nonholonomic andunderactuated control systems Some key concepts explained include formal defini-tions of underactuated and nonholonomic systems, as applied to mechanical systemsdescribed by general second order equations

1.2.1 Preliminaries

Definition of Underactuated and nonholonomic Systems

Definition 1.1 (Underactuated System) [10] Consider the affine mechanical systemdescribed by

¨

where q is the state vector of linearly independent generalized coordinates, f (·) is the vector field that captures the dynamics of the system, ˙q is the generalized velocity vector, G is the input matrix, and u is a vector of generalized inputs System (1.1) is

said to be underactuated if the external generalized inputs are not able to commandinstantaneous accelerations in all directions in the configuration space Formally

stated, this occurs if rank(G)< dim(q), where the dimension of q is usually defined

as the number of degrees of freedom of (1.1)

Definition 1.2 (Nonholonomic System) [10] Consider a mechanical system describedby

they can be integrated to constraints on the velocities, that is, if they can be pressed in the form

Stability

The concept of stabilizability is related to that of the existence of a feedback controllerfor a given system that will render the resulting closed loop system asymptoticallystable about an equilibrium point For linear systems, controllability implies sta-bilizability However, this is not true for the general nonlinear case A celebratedtheorem of Brockett [11] provides necessary conditions for smooth feedback stabiliz-ability Interested readers may refer to Appendix A and Appendix B on introduction

of constrained lagrangian equation and unicycle type wheeled mobile robot

Theorem 1.1 [11] Consider the system

with f (0, 0) = 0 and f (·, ·) continuously differentiable in a neighborhood of the gin If (1.5) is smoothly stabilizable, i.e., if there exists a continuously differentiable function g(x) such that the origin is an asymptotically stable equilibrium point of

ori-˙x = f (x, g(x)), with stability defined in the Lyapunov sense, then the image of f

must contain an open neighborhood of the origin.

1.3 Single Wheel Robot

1.3.1 Introduction

Gyrover is a single-wheeled gyroscopically-stabilized mobile robot developed at CarnegieMellon University [14]-[15] It is dynamically stable but statically unstable An inter-nal gyroscope is mounted to provide mechanical stabilization and steering capability.Gyroscope is a high speed, rotating wheel with three axes of freedom C the spinaxis (X), the precession axis (Y) and the applied torque axis (Z) According to thelaw of conservation of angular momentum, a heavy mass rotating at very high speedoffers large resistance to the rate of change of lean angle If such a rotating flywheel

is placed suitably inside a statically unstable mechanical structure, it stabilizes thestructure to balance and, therefore, gives it lateral stability The higher the rotatingspeed larger the resistance it provides to the change of lean angle If a torque isapplied to change the spin axis, the whole system then rotates around the third axisi.e the precession axis, and this motion is called precession Figure 1.1 illustratesthis mechanism of gyroscopic precession When the gravitational torque is appliedabout the Y axis to the wheel spinning about the X axis, it causes the wheel to rotateabout the Z axis

Therefore, when Gyrover leans to one side, rather than just fall over, the tationally induced torque causes the robot to precess so that it turns in the directionthat it is leaning Thus we could see the yaw and roll dynamics are highly coupled,

gravi-Figure 1.1: Example of Gyroscopic Effectimposing new challenges on the control and navigation of the robot The nature ofthe system is nonholonomic, nonlinear and underactuated.

On the other hand, such configuration conveys significant advantages over wheel, statically stable vehicles, including good dynamic stability and insensitivity

multi-to attitude disturbance; high maneuverability and low-rolling resistance Potentialapplications for Gyrover are numbers It can be used for space exploration where theabsence of aerodynamic disturbances and low gravity would permit efficient, high-speed mobility Because of its slim profile, it could be modified as a surveillancerobot to pass through doorways and narrow passages Another potential application

is as a amphibious vehicle if the mechanical structure is properly designed

1.3.2 Dynamic Model

The dynamic model of a single wheel robot can be obtained with a few assumptions

on its structure [16] They are:

1 wheel is assumed rigid

2 It is modeled as a homogeneous disk that rolled over a perfectly flat surfacewithout slip

3 The whole robot is modeled as a two-link manipulator, with the actuationmechanism suspended from the wheel bearing and a spinning disk attached atthe end of the second link

Four coordinates frames are assigned as follows (in Figure 1.2): (1) the inertiaframe PO, whose x-y-plane is anchored to the flat surface; (2) the body coordinateframe PB , whose origin is located at the center of the single wheel and whose z-

axis represents the axis of rotation of the wheel; (3) the coordinate frame of internalmechanismPC , whose center is located at point D and whose z-axis is always parallel

to z B; and (4) the flywheel coordinate frame PE, whose center is located at the

center of the Gyrover flywheel and whose z-axis represents the axis of rotation of the flywheel Note that y a is always parallel to y c

Figure 1.2: Coordinate of a rolling disk

Table 1.1: Gyrover Variable Definition

X c , Y c , Z c Coordinates of the center of mass of the robot w.r.t the inertia frame

α, β Precession and lean angle of the wheel respectively

β a tilt angle between the link l1 and z a-axis of the flywheel

γ, γ a Spin angles of the wheel and flywheel respectively

θ Angle between link l1 and x b-axis of the wheel

m ω , m i , m f Mass of the wheel, internal mechanism and flywheel respectively

m Total mass of the robot

R, r Radius of the wheel and the flywheel respectively

u1, u2 Drive torque from the drive motor and tilt torque from the tilt motor respectively

I xw , I yw , I zw Moment of inertia of the wheel about x B , y B , z B axes

I xf , I yf , I zf Moment of inertia of the flywheel about x a , y a , z a axes

µ s , µ g Friction coefficients in yaw and pitch directions respectively

Using the constrained Lagrangian method, the dynamic equation of the entiresystem is given by

β a θ

Equation (1.7) is the nonholonomic constraints

Understanding the characteristics of the robot dynamics is significant in thecontrol of the system A simplified model is easy to analyze Model of the singlewheel robot (Equations 1.6 - 1.8) is further simplified using the following steps:

1 Eliminate the Lagrange multipliers so that a minimum set of differential tions is obtained In this stage, the method of matrix partitioning, which issimilar in a manner to [13], is adopted.;

equa-2 l1 and l2 are assumed to be zero, thus the mass center of flywheel is coincident

with the center of the robot When we consider the steady motion of the robot,the internal mechanism hangs from the shaft with neglectable pendulum motion;

thus θ is set to zero;

3 The model is further simplified by decoupling the tilting variable β afrom

Equa-tion 1.6, since in practice, β a is directly controlled by the tilt motor and

as-suming that the motor is capable to track the desired β a (t) trajectory defined

in Equation 1.6 This is similar to the case of decoupling the steering variablefrom the bicycle dynamics in [17];

Let ˙β a as the new input u β a , S ββ a = sin(β + β a ), C ββ a = sin(β + β a) and

S 2ββ a = sin[2(β + β a)] Based on the previous model simplification and assumption,the dynamics becomes([16] and [18]):

˙β a = u β a

˜

M(˜ q)¨˜ q = F (˜˜ q, ˙˜ q) + ˜ B ˜ u (1.9)

fact that I xxf ¿ I xxw In reality, I xxf = 1

4m f r2 = 0.0015 is 200 times larger than

I xxw = 1

2m w R2 = 0.30625.

The above formulation is based on the assumption that system is rolling onflat surface The dynamics of the single-wheel robot on a inclined plane was first

introduced in [19] and the model including pitch dynamics was developed in [20].The corresponding linearized model was also developed therein.

1.3.3 Control Objectives and algorithm

The work on controller design is to a large extent objective-oriented Four majorobjectives has been so far identified as

1 Stabilization (also known as Balance Control)

2 Line-Tracking (also known as Path Following)

3 Position Control (also known as Point-to-Point Control)

4 Tilt-up Motion (also known as Fall recovery)

Stabilization

The target for stabilization control is to stabilize the lean angle β to a desired value and ˙β, ¨ β to zero A more critical challenge is to enable the robot to stand vertically,

i.e., to stabilize the lean angle β to π/2 and keep ˙β, ¨ β, ˙α, ˙γ to zero.

Stabilization of Gyrover was first studied in [21] A linearized model around the

vertical position was proposed based on the assumption that ˙γ a is sufficiently high so

that the terms without ˙γ a were discarded It is expressed as

The pitch dynamics is decoupled, thus it is controlled separately The yaw androll dynamics can be written in a linear state space form and a linear state feedbackcontrol law was proposed as follows:

u β a = −k1(δ β − δ β ref ) − k2˙δ β − k3( ˙α − ˙α ref) (1.20)

where k1 < 0, k2 < 0, k3 > 0 to ensure the asymptotic stability of the system

Sim-ulation results suggest the controller (1.20) is able to stabilize the robot toward/in

different lean angle, so as to control the precession rate( ˙α).

Note that the system is not controllable if ˙γ a = ˙γ = 0 This is because if the

single wheel robot is not rolling, it falls immediately

Another study on balance control is in [22], where three separate controllers wereproposed for three different cases based on Lyapunov method These three cases are

1) ˙α d is not zero(thus ˙γ d is not zero also); 2) both ˙α d and ˙γ d will be zero and 3) ˙α d will be zero while ˙γ d not ˙α d , ˙γ d , β d are some constant real numbers, which are the

target values for ˙α, ˙γ, β respectively.

For stabilization problem on inclined plane, a linear state backstepping feedbackcontroller for the linearized model developed on tilt plane, is proposed in [20].Position Control

The target for position control is to drive the robot from initial point to a set point,e.g., the origin in Cartesian space It is extremely important because it serves as thebasis for space tracking, required for any meaningful deployment of a mobile robot

The position control problem was dealt with in [23] and [24] The dynamic model

was transformed into the following form:

which involves the error distance e ≥ 0, measured from A to O(the origin of the frame) ψ = θ − α was defined as the angle measured between the vehicle principal axis and the distance vector e Then the following equations were obtained:

Figure 1.3: Parameters in Position Control

It was proved the controller was able to converge any initial state (e, β − π/2, ˙β)

starting from the domain D define by: D = {e(0), β(0) − π/2, ˙β(0)|e > 0, 0 < β < π,

of the single wheel robot is that not only the position (x, y) and the orientation θ, but also the lean angle β must be controlled with two control input While at the

same time, the lean angle must be kept within a stable region so that the robot doesnot fall over

The relationship of the steering rate and lean angle was first derived in [21] asfollows:

˙α ref = gmRδ β ref

(2I xxw + mR2)Ω0+ 2I xxf ˙γ a

(1.24)According to Equation (5.9), the key issue in path following is to track the lean angle

β ref that is compatible with the desired steering rate ˙α ref

Line tracking problem was first explored in [26] The position of contact point

on ground was used instead of the center of the wheel The input were also replaced

by the path curvature and contact point velocity because the motion of the contactpoint undergoes nonholonomic motion [27] The robot motion was described by a set

of configurations using the path curvature(κ), which can be expressed as,

κ(t) = ˙α(t)

v a (t) =

1

where r(t) is the radius of the curvature from the center of rotation to the contact

point and v a (t) is the velocity of contact point.

The line following controller was divided into two part for ease of control: (1)velocity control law and (2) torque control law, as a result of its nonholonomic natureand lateral instability

Torque control law is to generate the control signal(u β a) and is the same instabilization problem as equation (1.20) For stabilization problem, the robot is to

stand upright So the reference lean angle (β ref) is always 90 degrees But for

Figure 1.4: Line Following Principle Top Viewthe steering rate in Equation (5.9) and the steering rate relates with the radius ofcurvature in Equation (1.25).

One the other hand, under the nonholonomic constraints, the robot can onlyexecute a path with continuous path curvature and its path curvature is implicitlyrelated to the constraints Thus it becomes a better variable to describe the motioncontrol of the robot with nonholonomic constraints Therefore, based on [27], thevelocity control law was presented as follows:

dκ

ds = −aκ − b(ϕ − ϕ1) − cδ d (1.26)

where a, b, c are positive constants, ϕ1 and δ d are direction of the desired line and theperpendicular distance between the robot and the desired line respectively(Fig 1.4).Similar to the position control problem, a Lyapunov based feedback control law

for line tracking was given out in [24] and [25] It was demonstrated any initial state,

starting from [β(0) − π/2, ˙β(0), e(0), d(0)] with 0 < β(0) < π and e(0) > 0, converged

to the point [0, 0, 0, 0] T

Tilt-up Motion

One big advantage of this gyroscopically-stabilized single-wheeled robot is its ability

of recovery from fall According to the conservation of angular momentum, the robot

is able to recover from fall by tilting the flywheel The tilting direction of flywheelopposes to the leaning direction of robot As both traditional single track vehicle andfour-wheeled vehicles are unable to do so, [28] is the first published work on such kind

of tilt-up motion so far

Control of tilt-up motion is to control a robot to the vertical position from anyinitial lean angle Normally, there are two cases according to the robot’s initialconfiguration

1 Robot rolling without slip

2 Robot lying on the ground without rolling

In the first case, the tilt-up motion is in fact the same as the aforementioned bilization problem For the second case, the previous developed model is invalid todescribe this type of tilt-up motion because the rolling speed of the wheel is zeroand the robot is statically lying on the ground, and hence, it violates the assumption

sta-of the unmodeled parameters, such as friction and coriolis force, are relatively moresignificant to such a system than a static or quasi-static system, during the tilt-upmotion The complexity in modeling such a system makes the design of model-basedcontrol scheme extremely difficult.

On the other hand, it turned out a skilled operator can control the tilt-up tion of the robot very well Therefore, a human control strategy (HSC) model wastrained in [29] to abstract the operator’s skill The flexible cascade neural networkarchitecture with node-decoupled extended Kalman filtering (NDEFK) was used formodeling the realtionship between human operator’s control command and the statevariables of the robot The operator’s control commands were the drive torque and

mo-tilt torque (β, ˙β, β a , ˙β a , ˙α, ˙γ) were selected as state variables Base on this, a

human-based controller was developed for the automatic control of the tilt-up motion [15]

1.3.4 Others

Beside the above-mentioned contents, there have been some other works on this type

of robot reported in literature Another similar single-wheel robot was developed inUniversity of Florida [30] W Nuku [31] developed the dynamic model of the robotusing Kane’s method For the robot dynamics on inclined plan, the dynamic modelunder such circumstance and corresponding linearized model at the vertical position

is presented in [32] A backstepping-based controller was developed therein such thatthe robot can be stabilized remaining perpendicular to the surface while rolling up

The condition of rolling up and methods to drive the robot up when the condition ofrolling up fails were studied in [33].

Innovative design of platforms is an important aspect of building automation androbotic systems that can match the recent advances in artificial intelligence and sys-tem control Two-legged walkers [34], hoppers [35], wheeled robot [36][37] and othersare all motivated by the demand to increase mobility and flexibility of the platform

to be applied to different environments

Various structures of wheeled mobile robot (WMR) with different numbers ofwheels, different choices of steering etc have been studied by the researchers in lasttwo decades Improving the maneuverability and steering capacity of WMR hasalways been key consideration in these efforts Works published in [36][37] adopt thedesign using three drive centered wheels that can be steered Robots or autonomousvehicles with multiple wheels provide excellent static stability achieved by keeping thegravity vector through the center of mass inside its polygon of support Such systemsare built using relatively rigid members and can be controlled based on kinematicconsiderations

However, during dynamic locomotion, the inertial forces become significant incom- parison to the gravitational forces Dynamic effects are more prominent athigh speed of motion and when dynamic disturbances, such as rough terrain, are

high Large polygon of support, usually desired for static stability, causes dynamicinstability in these situations For example, when a four-wheeled vehicle with largepolygon of support passes over a bump, the dynamic disturbance at the wheel cangenerate a torque large enough to topple the vehicle Dynamic stability is an impor-tant issue in the design of mobile robots capable of moving at high speed Dynamicstability can be improved by either controlling the support points through active sus-pension or by controlling the attitude of the vehicle On the other hand, Brachiator[38] and Acrobot [39] are two of few examples where dynamic stability is achieved byexploiting the motion of the system.

Bicycle, motorcycle etc are some of the practical machines where dynamic ity is exploited for useful purpose A two-wheeled bicycle or motor cycle is staticallyunstable in its roll direction, but their dynamic stability at moderate or high speed is

stabil-a well-known phenomenon Gyroscopic stabil-action of the steered front wheel stabil-and propersteering geometry guarantees dynamic stability This phenomenon can be mimicked

to design a dynamically stabilized vehicle capable of maneuvering at very high speed.Development of a self-contained unicycle with pitch and roll stability was presented in[40] The researchers at the Carnegie Melon University developed and named it Gy-rover, a gyroscopically stabilized single wheel robot with excellent dynamic stability[14][28][16][15] The most important component of this design is a flywheel of heavymass hung from the axle of the wheel The flywheel spinning at high speed providesgyroscopic forces required for mechanical stability as well as the capability to steer

the wheel Good maneuverability with zero-turning radius, high speed of motion,ability to navigate in rough terrains, and fall recovery achieved for this design provedclear advantage over previous designs of wheeled and legged platforms.

The main objective of the research presented in this thesis is to design, ment and control of a gyroscopically-stabilized single wheel robot in a comprehensivemanner, in which it tries to cover the issues and considerations from where the re-quirements were set

imple-Both hardware and software development are discussed in this thesis, aimed toprovide dynamic stability and autonomous sensing and control for rapid locomotion.The design follows the idea conceived by CMU researchers and we build our own robot

- Gyrobot Various sensors, powerful computing board and real-time operating system

are integrated for reliable sensing and automatic control Different control themes tostabilize the system and track desired trajectories under various environment havebeen proposed On the other hand, mechatronic design approach with virtual robotsimulator and controller development are also explored

This thesis is organized as follows:

The process of Gyrobot design and implementation are presented in Chapter 2.Three prototypes were built The first one, Gyrobot I, consists of the basic mechani-cal structure, actuators and drives and can be controlled manually Two subsequent

prototypes are equipped with PC014 boards to implement sensor data acquisitionand autonomous control ability Considerations on motor selection and componentslocation are presented for better stability performance and maneuver capability Vi-bration reduction measures follows, with an aim to highlight the practical challenges

in mechatronic system realization Experiment results are presented for each type, pertaining to the design objective

proto-Software design and implementation for Gyrobot are presented in Chapter 3.QNX real-time OS is chosen as the platform for Gyrobot for its multitasking and fastcontext switching capabilities The entire software system consists of a main block,

in which functional threads are scheduled and controlled Details for each task thread

is also given with system setup procedures

Dynamic model and virtual 3D model of the Gyrobot are illustrated in Chapter

4 Following the Lagrangian approach, two critical problems in the dynamic modelingprocess are investigated with detailed derivation The model is linearized for controllerdesign A virtual 3D simulator, an essential part of mechatronic design approach, isdeveloped for improving mechanical structure and controller design and simulation.Two tracking control algorithms are proposed in Chapter 5 Three key equationsdominating the motion of Gyrobot are identified The virtual robot approach creates areference velocity generator for kinematic control The control law is able to drive therobot to follow a predefined straight line, a circle with desired radius and sinusoidalpath

Conclusion and recommendations for future work are presented in Chapter 6.

man-Gyrobot III is the latest prototype in which some components are relocated and

a new spin motor is installed for better stability performance The vibration issue

is also addressed in this prototype for stable sensor reading Experiment results aregiven for each prototype pertaining to the design objective.

Gyrobot I [41] is the first prototype developed for this research to verify the conceptand workability of the robot configuration It is designed according to the sameprinciple used to design CMU Gyrover; however, it includes some modifications inthe actuation mechanism required to generate forward and backward motion

2.2.1 Mechanical Design

The design began by using the specifications of the rover built in University of Florida[30] The gyro flywheel and the shaft are machined from a single piece of carbonsteel, as shown in Figure 2.1 Since the flywheel is required to rotate at very highspeed (about several thousand RPM), eccentricity of any small amount can causesevere undesirable vibration That’s why the shaft and the flywheel are machinedfrom a single piece of carbon steel instead of mounting the flywheel on the shaft.The drawback of this approach lies with the fact that the whole flywheel has to bereplaced in case of shaft failure Diameter and thickness of the flywheel are 89mmand 25mm The inner and outer diameters of the ball bearing used to mount theflywheel on the inner are 6mm and 12mm The 3D view of the inner gimbal withflywheel assembly and the entire inner mechanism is shown in Figures 2.2 and Figure

Figure 2.1: Gyrobot I Flywheel

Figure 2.2: Gyrobot I Inner Gimbal and

Flywheel Assembly Figure 2.3: Gyrobot I Inner Mechanism

As a first attempt, the gimbal structure was built using wood and epoxy tokeep the design and fabrication simple However, such materials turned out to beunsuitable for flywheel spinning at very high RPM The working prototype usedheavy plastic and screw joints, so the design is kept simple by using two identicalstructures screwed together.

Two pieces of plastic light shades are used to make the outer shell of Gyrobot

I The components are firstly assembled with the central shaft of the Gyrobot Ipassing through the upper segment of the outer gimbals, and the entire mechanics isthen mounted inside this shell Two pieces of the shell are joined together using highdensity foam

2.2.2 Actuation Mechanism

As described in Chapter I, the Gyrobot I stabilizes itself by the angular momentumprovided by the fast-spinning of the internal flywheel The steering capability isachieved by the tilting of internal flywheel while the forward/backward motion isachieved by deploying a third drive motor These three motors are effectuated bythree separate motors, namely spin motor, tilt motor and drive motor

Flywheel Spinning Motion

The spin motor of Gyrobot I is a DC type servo motor It is fitted at one side of theinner gimbal and align to the center of the flywheel, which is the spinning axis Acounter weight, which is a cylindrical iron piece, is deployed on the other side of the

inner gimbal to balance inner gimbal The introduction of counter weight minimizethe consistent tilting motion observed in the initial test Tachometer reading showsthe spin motor is able to provide 3000 rpm at its maximum power.

Flywheel Tilting Motion

Steering of the Gyrobot I is accomplished by applying tilt torque on the flywheel Thetilt motion is achieved by altering the spinning direction, which means the tilt torque

is applied to the flywheel roll direction Since the flywheel speed is around 3000 rpmwith a mass of 1kg, large torque is required from the tilt motor while maintaining theresponse agility A RC servo motor best fits in such application scenario Controlled

by PPM signal, the motor responses to the position signal by its internal circuit Agear train with 4:1 ratio is also mounted to further increase the torque that is applied

on the flywheel

Wheel Forward/Backward Motion

In the design of CMU Gyrover [14],[16],[18] and UF Gyrobot [30], the forward andbackward rotation of the wheel is achieved utilizing the acceleration/decelerationproduced by displacing the hanging mass from its equilibrium position This is ac-complished by applying torque from the drive motor which swings the hanging mass.Subject to the gravitational force, the hanging mass tends to return to the equilibriumposition which is directly below the central shaft Since the mass of inner mechanism

is much heavier, the outside shell rotates leading to the movement of the entire device

Our design, on the other hand, employs a simpler technique for actuation Shaft

or axle of the Gyrobot I can move freely inside the outer gimbals assembly, and its twoends are fixed to the rim and wheel Torque is applied by the drive motor directly tothe central shaft and accordingly rotates the wheel that enables the forward/backwardmotion Since the inner mechanism is hanged freely on the central shaft, it will not

be affected by this movement and will remain vertical due to its larger mass It isillustrated in Figure 2.4, as the drive torque is

where mg is the weight of the pendulum mass and Lsinθ is the effective length (L=length of the link).

Our design, on the contrary, drives the central axle of the wheel directly, instead

of applying torque to the hanging pendulum mass, as shown in Figure 2.5 Therefore,the torque to produce acceleration is no more related to the mass of the pendulum,but depends on the power of the drive motor As far as the speed of the wheel isconcerned, it is not limited by the drive motor in the CMU design where the wheel

is driven indirectly but it is limited in our case For the CMU design, the Gyrovercontinues to accelerate as long as a torque is maintained In our design, the maximumspeed of the Gyrobot is restricted by the maximum speed of the drive motor A betterspeed control shall be achieved through our design approach

In Gyrobot I, the drive motor is of DC servo type Since output of the RC

re-Figure 2.4: CMU Gyrobot Driving

Con-cept Figure 2.5: NUS Gyrover Driving Conceptceiver is PPM wave, a DC motor drive is fitted between the receiver and the motors

to convert the PPM wave into corresponding DC voltage However, the final mentation is that two stepper motors are used in tandem to produce the drive torquedue to the breakage of the original DC motor A new one will be installed in GyrobotII

imple-2.2.3 Experiment

The completed Gyrobot I is shown in Figure 2.6 with illustration of the componentsthat fitted inside the shell Table 2.1 gives the mechanical parameters of completedGyrobot I

Table 2.1: Mechanical Parameters of Gyrobot One

Mass(kg) Diameter(mm) Thickness(mm)

Figure 2.6: Gyrobot I Componentsright but showed slow-speed precession though no tilt torque was applied This wascaused due to imperfect machining of different components and their assembly whichintroduced small amount of mechanical eccentricity, and therefore, tilt torque wasgenerated This finding was verified by applying a constant tilt torque to nullifythe eccentricity, and the Gyrobot I was able to stay upright without showing veryminimum sign of precession or toppling, as shown in Figure 2.7

The second experiment was carried out to test the driving capability of theGyrobotI, as shown in Figure 2.8 The experiments results were stored in video andexhibited expected results Forward/backward motion was achieved It also exhibitedsteering capability when the flywheel was manually tilted

Figure 2.7: Gyrobot I Stability Test

Figure 2.8: Snapshots of Gyrobot I Running Test

2.2.4 Conclusion

Gyrobot I is the first realization of the working vehicles Feasibility of the ing concept has been verified through basic analysis and several experiments Theseresults have proven the concept workable and have verified many of the expectedadvantages On the other side, the limitation of Gyrobot I is also obvious It canonly be steered by human operation through a RC radio, with no autonomous capa-bility The step motors are provisional replacement of the broken-down DC motorand are not able to provide sufficient power for fast maneuver These shortcomingswill be addressed in Gyrobot II, which is brought out in the next phase of this de-velopment Various components are installed for autonomous operation Meanwhile,human interface using remote control is still installed in the 2nd prototype

Gyrobot II is the second prototype that has been built The target for this prototype

is to implement the hardware and software that enable both autonomous operation

as well as human operation To this end, several sensors have been mounted onboard

to measure the environment and robot status A computing board and data tion card are also installed to handle the on-board autonomous sensing and control,with greatly enhanced computing capability For simplicity, Gyrobot IIinherits themechanical structure that had been verified in Gyrobot I Details of the softwaredesign will be described in Chapter 3

acquisi-Figure 2.9 illustrates the hardware components and connection structure signed to fulfill the task of autonomous excavation for Gyrobot II It consists of foursubsystems, namely:

de-• Computing and Data Acquisition Subsystem

• Power and Actuation Subsystem

• Sensor Subsystem

• Human Operation Subsystem

Figure 2.9: Gyrobobt II Block Diagram

2.3.1 Computing and Data Acquisition Subsystem

This subsystem consists of a CPU board and a data acquisition card, both of PC104

an all-in-one CPU module with two-on-board 10/100 BaseT Ethernet interfaces TheCPU is National Semiconductor Geode MMX, available with speeds up to 300MHz.

It is a 64-bit microprocessor, compatible with mainstream x86 software, e.g., QNXoperating systems which is used in Gyrobot The board is also a self-containedcomputer system, with graphic card and memory interface One highlight of theboard is the energy-saving feature it possess When running at full speed, the powerrequired is only about 6W This features its feasibility with application in embeddedrobotic system

A Compact Flash (CF) card is deployed as the system main storage, for executingimages and saving data files Hard disk is excluded as an option because of itslarge size and vulnerability against vibration, which is not avoidable due to the fast-spinning flywheel

The data acquisition card is DIAMMOND-MM-32-AT board with a full set offeatures, shown in Figure 2.11 It offers total 32 analog inputs with 16-bit resolutionand programmable input range with 200,000 samples per second maximum samplingrate with FIFO operation A 32-bit counter/timer is installed for A/D conversion andinterrupt timing And one 16-bit counter/timer for general purpose use It also offersthe additional important feature of auto-calibration for both analog input and outputchannels The board is used to read the feedback from the sensor subsystems, performthe control algorithm and generate the control signal to actuation subsystems