Stability Augmentation of Two-Wheeled Robots on Pedestrian Terrain

Abstract

Wheeled robots, which are expected to be a beneficial and revolutionary mechanism for the next generation robotic systems, have gained worldwide attention from research communities. In this dissertation, statically unstable two-wheeled Robots (TWRs) are studied on pedestrian terrain. The pedestrian terrain includes flat horizontal footpaths, ramps and uneven terrain, for example, bumps. The primary issue faced by statically unstable twowheeled robots on these terrains is the instability due to only one contact point of the robot wheel to the ground, which reduces normal force and the wheel motion or any kind of tiny disturbance that causes the robot body to fall. Thus, stability augmentation and performance enhancement of TWRs on the ramps and bumps, a major control challenge faced by the TWR users and researchers, requires control design along with the stability analysis of the closedloop TWR system and dynamics modelling. In this thesis a linear, a semi-nonlinear and a nonlinear control scheme for statically unstable TWRs is proposed for the motion on horizontal, inclined and uneven terrain scenario considering the availability of feedback of the system states. The main issues that are analysed in depth in this research are the effects of terrain inclination on stability and performance of the TWRs, the dynamics of TWR motion on horizontal, inclined and uneven terrain, control synthesising, stability and the stability region of closed-loop dynamics of TWRs. Furthermore, the equations of motion in three scenarios have been derived using the Lagrangian method, which is a new contribution to the statically unstable TWRs. The performance analysis of transient response has been carried out with simple PD and LQR controllers. The LQR is utilised, later, as a baseline controller and the Gain-Scheduled (GS) controller is designed based on the assumption that the wheel-terrain contact angle is known. The control is implemented for non-horizontal, inclined and uneven, terrain. Another novel controller proposed and synthesized in this dissertation is the Control Lyapunov Function Based Controller (LFBC) for motion of TWRs on all the three terrain, which is a new contribution to the TWRs. The proposed CLF based control schemes aim to perform control authority robustly with guaranteed asymptotic stability and with a wider stability region to enhance the performance and to augment the stability of TWRs on pedestrian terrain. It is proved through simulations that GS control is a good choice for inclined terrain, compared to the linear optimal controller, the LFBC is proven to be an optimal choice to solve the non-linear control problems of TWR on pedestrian terrain to augment their stability. Another contribution of this research is in the field of control implementation on a physical real time two-wheeled robot. Real time implementation is presented with many challenges in terms of reliability and accuracy of information from sensors in measuring the states and the wheel-terrain contact angle. The novel and simple terrain inclination measuring scheme based on wheel encoders is proposed, which detects the absolute position of the wheel whilst a wheel-terrain contact angle is determined online from known function of the terrain. By applying controllers at different speeds of the TWR the effectiveness and reliability of the proposed scheme is proved. All the proposed algorithms have been investigated through simulations as well as real time implementation under different initial conditions to validate the significance and effectiveness of them for the performance regulation and velocity tracking.