Robust Stabilization of a Wheeled Mobile Robot Using Model Predictive Control Based on Neurodynamics Optimization

In this paper, a robust model predictive control (MPC) scheme using neural network based optimization has been developed to stabilize a physically constrained mobile robot. By applying a state scaling transformation, the intrinsic controllability of a mobile robots can be regained by incorporation into the control input with an additional exponential decaying term. An MPC based control method is then designed for the robot in the presence of external disturbances. The MPC optimization has been formulated as a convex nonlinear minimization problem and a primal-dual neural network (PDNN) is adopted to solve this optimization problem over a finite receding horizon. The computational efficiency of MPC has been significantly improved by the proposed neuro-dynamic approach. Experimental studies under various dynamic conditions have been performed to demonstrate the performance of the proposed approach, which can be applied for a large range of wheeled mobile robots

Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

Model Predictive Control of Nonholonomic Mobile Robots

In this work, we investigate the possibility of using model predictive control (MPC) for the motion coordination of nonholonomic mobile robots. The contributions of this dissertation can be summarized as follows.A robust formation controller is developed for the leader-following formation of unmanned aerial vehicles (UAVs). With the assumption that an autopilot operating in holding mode at the low-layer, we present a two-layered hierarchical control scheme which allows a team of UAVs to perform complex navigation tasks under limited inter-vehicle communication. Specifically, the robust control law eliminates the requirement of leader's velocity and acceleration information, which reduces the communication overhead.A dual-mode MPC algorithm that allows a team of mobile robots to navigate in formations is developed. The stability of the formation is guaranteed by constraining the terminal state to a terminal region and switching to a stabilizing terminal controller at the boundary of the terminal region. With this dual-mode MPC implementation, stability is achieved while feasibility is relaxed.A first-state contractive model predictive control (FSC-MPC) algorithm is developed for the trajectory tracking and point stabilization problems of nonholonomic mobile robots. The stability of the proposed MPC scheme is guaranteed by adding a first-state contractive constraint and the controller is exponentially stable. The convergence is faster and no terminal region calculation is required. Tracking a trajectory moving backward is no longer a problem under this MPC controller. Moreover, the proposed MPC controller has simultaneous tracking and point stabilization capability.Simulation results are presented to verify the validity of the proposed control algorithms and demonstrate the performance of the proposed controllers.School of Electrical & Computer Engineerin

Nonprehensile Manipulation of an Underactuated Mechanical System With Second-Order Nonholonomic Constraints: The Robotic Hula-Hoop

A mechanical system consisting of a hoop and a pole is considered, for which the corresponding dynamic model represents an underactuated system subject to second-order nonholonomic constraints. The pursued goal is to simultaneously track a trajectory in the unactuated coordinates and to stabilize the actuated ones. For the model under consideration, the well-known noncollocated partial feedback linearization algorithm fails since the corresponding zero dynamics is unstable. In this work, we show that the actuated coordinates, i.e., the pole can be stabilized by exploiting the null space of the coupling inertia matrix without affecting the performance in the underactuated coordinates tracking. We present a formal mathematical analysis, which guarantees ultimate boundedness of all coordinates. Performed simulations bolster the proposed approach

An observer-based type-3 fuzzy control for non-holonomic wheeled robots

Non-holonomic wheeled robots (NWR) comprise a type of robotic system; they use wheels for movement and offer several advantages over other types. They are efficient, highly, and maneuverable, making them ideal for factory automation, logistics, transportation, and healthcare. The control of this type of robot is complicated, due to the complexity of modeling, asymmetrical non-holonomic constraints, and unknown perturbations in various applications. Therefore, in this study, a novel type-3 (T3) fuzzy logic system (FLS)-based controller is developed for NWRs. T3-FLSs are employed for modeling, and the modeling errors are considered in stability analysis based on the symmetric Lyapunov function. An observer is designed to detect the error, and its effect is eliminated by a developed terminal sliding mode controller (SMC). The designed technique is used to control a case-study NWR, and the results demonstrate the good accuracy of the developed scheme under non-holonomic constraints, unknown dynamics, and nonlinear disturbances