Feedback Linearization Techniques for Collaborative Nonholonomic Robots

Collaborative robots performing tasks together have significant advantages over a single robot. Applications can be found in the fields of underwater robotics, air traffic control, intelligent highways, mines and ores detection and tele-surgery. Collaborative wheeled mobile robots can be modeled by a nonlinear system having nonholonomic constraints. Due to these constraints, the collaborative robots arc not stabilizable at a point by continuous time-invariant feedback control laws. Therefore, linear control is ineffective, even locally, and innovative design techniques are needed. One possible design technique is feedback control and the principal interest of this thesis is to evaluate the best feedback control technique. Feedback linearization is one of the possible feedback control techniques. Feedback linearization is a method of transforming a nonlinear system into a linear system using feedback transformation. It differs from conventional Taylor series linearization since it is achieved using exact coordinates transformation rather than by linear approximations of the system. Linearization of the collaborative robots system using Taylor series results in a linear system which is uncontrollable and is thus unsuitable. On the other hand, the feedback linearized control strategies result in a stable system. Feedback linearized control strategies can he designed based on state or input, while both state and input linearization can be achieved using static or dynamic feedback. In this thesis, a kinematic model of the collaborative nonholonomic robots is derived, based on the leader-follower formation. The objective of the kinematic model is to facilitate the design of feedback control strategies that can stabilize the system and Minimize the error between the desired and actual trajectory. The leader-follower formation is used in this research since the collaborative robots are assumed to have communication capabilities only. The kinematic model for the leader-follower formation is simulated using MATLAB/Simulink. A comparative assessment of various feedback control strategies is evaluated. The leader robot model is tested using five feedback control strategies for different trajectories. These feedback control strategies are derived using cascaded system theory, stable tracking method based on linearization of corresponding error model, approximation linearization, nonlinear control design and full state linearization via dynamic feedback. For posture stabilization of the leader robot, time-varying and full state dynamic feedback linearized control strategies are used. For the follower robots using separation bearing and separation-separation formation, the feedback linearized control strategies are derived using input-output via static feedback. Based on the simulation results for the leader robot, it is found that the full state dynamic feedback linearized control strategy improves system performance and minimizes the mean of error more rapidly than the other four feedback control strategies. In addition to stabilizing the system, the full state dynamic feedback linearized control strategy achieves posture stabilization. For the follower robots, the input-output via static feedback linearization control strategies minimize the error between the desired and actual formation. Furthermore, the input-output linearized control strategies allow dynamical change of the formation at run-time and minimize the disturbance of formation change. Thus, for a given feasible trajectory, the full state feedback linearized strategy for the leader robot and input-output feedback linearized strategies for the follower robots are found to be more efficient in stabilizing the system

Distributed formation tracking control of multiple car-like robots

In this thesis, distributed formation tracking control of multiple car-like robots is studied. Each vehicle can communicate and send or receive states information to or from a portion of other vehicles. The communication topology is characterized by a graph. Each vehicle is considered as a vertex in the graph and each communication link is considered as an edge in the graph. The unicycles are modeled firstly by both kinematic systems. Distributed controllers for vehicle kinematics are designed with the aid of graph theory. Two control algorithms are designed based on the chained-form system and its transformation respectively. Both algorithms achieve exponential convergence to the desired reference states. Then vehicle dynamics is considered and dynamic controllers are designed with the aid of two types of kinematic-based controllers proposed in the first section. Finally, a special case of switching graph is addressed considering the probability of vehicle disability and links breakage

Comprehensive review on controller for leader-follower robotic system

985-1007This paper presents a comprehensive review of the leader-follower robotics system. The aim of this paper is to find and elaborate on the current trends in the swarm robotic system, leader-follower, and multi-agent system. Another part of this review will focus on finding the trend of controller utilized by previous researchers in the leader-follower system. The controller that is commonly applied by the researchers is mostly adaptive and non-linear controllers. The paper also explores the subject of study or system used during the research which normally employs multi-robot, multi-agent, space flying, reconfigurable system, multi-legs system or unmanned system. Another aspect of this paper concentrates on the topology employed by the researchers when they conducted simulation or experimental studies

Feedback Linearization Techniques for Collaborative Nonholonomic Robots

Collaborative robots performing tasks together have significant advantages over a single robot. Applications can be found in the fields of underwater robotics, air traffic control, intelligent highways, mines and ores detection and tele-surgery. Collaborative wheeled mobile robots can be modeled by a nonlinear system having nonholonomic constraints. Due to these constraints, the collaborative robots arc not stabilizable at a point by continuous time-invariant feedback control laws. Therefore, linear control is ineffective, even locally, and innovative design techniques are needed. One possible design technique is feedback control and the principal interest of this thesis is to evaluate the best feedback control technique. Feedback linearization is one of the possible feedback control techniques. Feedback linearization is a method of transforming a nonlinear system into a linear system using feedback transformation. It differs from conventional Taylor series linearization since it is achieved using exact coordinates transformation rather than by linear approximations of the system. Linearization of the collaborative robots system using Taylor series results in a linear system which is uncontrollable and is thus unsuitable. On the other hand, the feedback linearized control strategies result in a stable system. Feedback linearized control strategies can he designed based on state or input, while both state and input linearization can be achieved using static or dynamic feedback. In this thesis, a kinematic model of the collaborative nonholonomic robots is derived, based on the leader-follower formation. The objective of the kinematic model is to facilitate the design of feedback control strategies that can stabilize the system and Minimize the error between the desired and actual trajectory. The leader-follower formation is used in this research since the collaborative robots are assumed to have communication capabilities only. The kinematic model for the leader-follower formation is simulated using MATLAB/Simulink. A comparative assessment of various feedback control strategies is evaluated. The leader robot model is tested using five feedback control strategies for different trajectories. These feedback control strategies are derived using cascaded system theory, stable tracking method based on linearization of corresponding error model, approximation linearization, nonlinear control design and full state linearization via dynamic feedback. For posture stabilization of the leader robot, time-varying and full state dynamic feedback linearized control strategies are used. For the follower robots using separation bearing and separation-separation formation, the feedback linearized control strategies are derived using input-output via static feedback. Based on the simulation results for the leader robot, it is found that the full state dynamic feedback linearized control strategy improves system performance and minimizes the mean of error more rapidly than the other four feedback control strategies. In addition to stabilizing the system, the full state dynamic feedback linearized control strategy achieves posture stabilization. For the follower robots, the input-output via static feedback linearization control strategies minimize the error between the desired and actual formation. Furthermore, the input-output linearized control strategies allow dynamical change of the formation at run-time and minimize the disturbance of formation change. Thus, for a given feasible trajectory, the full state feedback linearized strategy for the leader robot and input-output feedback linearized strategies for the follower robots are found to be more efficient in stabilizing the system