Chapter Background and Literature Review 1.1 Mobile Wheeled Robot: A Historical Perspective Most mobile machines and, particularly mobile robots, roll on wheels [1]. Although legged and treaded locomotion were intensively studied and corresponding mobile robots were developed in the last decade, it is commonly accepted that “wheeled mobile robots are more energy-efficient than legged or treaded robots on hard, smooth surface”[2]. Wheeled robots are mechanically simple and easy to construct. “Wheels are 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 capable of locomotion on a surface solely through the actuation of wheel assemblies mounted on the robot and in contact with the surface. A wheel assembly is a device which 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 reported 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 of wheeled vehicles: ordinary car-like robots (including passenger cars, single unit trucks, single unit buses, and articulated trucks); dual drive robots (dual drive motors with various casters); synchronous drive and steering robots; and omni-directional robots. Rajagopalan [6] analyzed the kinematics of WMR with various combinations ofdriving and steering wheels. It was shown that for driverless ground vehicles (WMRs) operating at low speed ([...]... and assumption, the dynamics becomes( [16 ] and [18 ]): ˙ βa = uβa ˜ q ¨ ˜ q ˜ ˜˜ ˙ M (˜)q = F (˜, q ) + B u ˜ 13 (1. 9) with   α q = β  ˜ γ ˜  ˜ M 11 0 M13 ˜  M =  0 Ixf + Ixw + mR2 0 2 ˜ M13 0 2Ixw + mR ˜  F1 ˜ ˜ F = F2  ˜ F3 ˜ B = 0 0 1 u1 ˜ 12 0 0 , u = uβa B (1. 10) (1. 11) (1. 12) (1. 13) 2 2 2 ˜ M 11 = Ixf + Ixw + Ixw Cβ + mR2 Cβ + Ixf Cββa (1. 14) ˜ M13 = 2Ixw Cβ + mR2 Cβ (1. 15) ˙ ˙˙ ˜ F1... vehicle Dynamic stability is an important issue in the design of mobile robots capable of moving at high speed Dynamic stability can be improved by either controlling the support points through active suspension 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 by exploiting the motion of the... rotation to the contact point and va (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 nature and lateral instability Torque control law is to generate the control signal(uβa ) and is the same in stabilization problem as equation (1. 20) For stabilization problem,... −µg Ω + u1 where β = 900 + δβ , γ = Ω0 + Ω and βa = δβa ˙ 15 (1. 19) The pitch dynamics is decoupled, thus it is controlled separately The yaw and roll dynamics can be written in a linear state space form and a linear state feedback control law was proposed as follows: ˙ ˙ ˙ uβa = −k1 (δβ − δβref ) − k2 δβ − k3 (α − αref ) (1. 20) where k1 < 0, k2 < 0, k3 > 0 to ensure the asymptotic stability of the system... 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 Gyrover, 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 heavy mass hung from the axle of. ..Figure 1. 2: Coordinate of a rolling disk Table 1. 1: Gyrover Variable Definition Xc , Yc , Zc α, β βa γ, γa θ mω , m i , m f m R, r u1 , u 2 Ixw , Iyw , Izw Ixf , Iyf , Izf µs , µ g Coordinates of the center of mass of the robot w.r.t the inertia frame Precession and lean angle of the wheel respectively tilt angle between the link l1 and za -axis of the flywheel Spin angles of the wheel and flywheel... β ,λ =    λ2 k1 γ    0  βa  k2 θ (1. 8)  0 0  0  u1  , 0 , u =  u2 0  1 0 Equation (1. 7) is the nonholonomic constraints Understanding the characteristics of the robot dynamics is significant in the control of the system A simplified model is easy to analyze Model of the single wheel robot (Equations 1. 6 - 1. 8) is further simplified using the following steps: 1 Eliminate the Lagrange... between link l1 and xb -axis of the wheel Mass of the wheel, internal mechanism and flywheel respectively Total mass of the robot Radius of the wheel and the flywheel respectively Drive torque from the drive motor and tilt torque from the tilt motor respectively Moment of inertia of the wheel about xB , yB , zB axes Moment of inertia of the flywheel about xa , ya , za axes Friction coefficients in yaw and pitch... mechanical stability as well as the capability to steer 24 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 proved clear advantage over previous designs of wheeled and legged platforms The main objective of the research presented in this thesis is to design, implement and control of a gyroscopically-stabilized... integrated for reliable sensing and automatic control Different control themes to stabilize the system and track desired trajectories under various environment have been proposed On the other hand, mechatronic design approach with virtual robot simulator and controller development are also explored 1. 5 Thesis Outline This thesis is organized as follows: The process of Gyrobot design and implementation are presented . becomes( [16 ] and [18 ]): ˙ β a = u β a ˜ M(˜q) ¨ ˜q = ˜ F (˜q, ˙ ˜q) + ˜ B˜u (1. 9) 13 with ˜q =   α β γ   (1. 10) ˜ M =   ˜ M 11 0 ˜ M 13 0 I xf + I xw + mR 2 0 ˜ M 13 0 2I xw + mR 2   (1. 11) ˜ F. =   ˜ F 1 ˜ F 2 ˜ F 3   (1. 12) ˜ B =  0 0 1 ˜ B 12 0 0  , ˜u =  u 1 u β a  (1. 13) ˜ M 11 = I xf + I xw + I xw C 2 β + mR 2 C 2 β + I xf C 2 ββ a (1. 14) ˜ M 13 = 2I xw C β + mR 2 C β (1. 15) ˜ F 1 =. Chapter 1 Background and Literature Review 1. 1 Mobile Wheeled Robot: A Historical Perspec- tive Most mobile machines and, particularly mobile robots, roll on wheels [1] . Although legged and treaded