Sensitivity analysis of hybrid systems with state jumps with application to trajectory tracking

This paper addresses the sensitivity analysis for hybrid systems with discontinuous (jumping) state trajectories. We consider state-triggered jumps in the state evolution, potentially accompanied by mode switching in the control vector field as well. For a given trajectory with state jumps, we show how to construct an approximation of a nearby perturbed trajectory corresponding to a small variation of the initial condition and input. A major complication in the construction of such an approximation is that, in general, the jump times corresponding to a nearby perturbed trajectory are not equal to those of the nominal one. The main contribution of this work is the development of a notion of error to clarify in which sense the approximate trajectory is, at each instant of time, a firstorder approximation of the perturbed trajectory. This notion of error naturally finds application in the (local) tracking problem of a time-varying reference trajectory of a hybrid system. To illustrate the possible use of this new error definition in the context of trajectory tracking, we outline how the standard linear trajectory tracking control for nonlinear systems -based on linear quadratic regulator (LQR) theory to compute the optimal feedback gain- could be generalized for hybrid systems

Nonlinear H_inf -Control of Mechanical Systems under Unilateral Constraints on the Position

6 pagesNational audienceThe work focuses on the study of hybrid mechanical systems under unilateral constraints on the position. The problem of robust control of mechanical systems is addressed under unilateral constraints by designing a nonlinear H-infinity -controller developed in the nonsmooth setting, covering impact phenomena. Performance issues of the nonlinear H-infinity-tracking controller are illustrated in a numerical simulation

Discrete Mechanics and Optimal Control Applied to the Compass Gait Biped

This paper presents a methodology for generating locally optimal control policies for simple hybrid mechanical systems, and illustrates the method on the compass gait biped. Principles from discrete mechanics are utilized to generate optimal control policies as solutions of constrained nonlinear optimization problems. In the context of bipedal walking, this procedure provides a comparative measure of the suboptimality of existing control policies. Furthermore, our methodology can be used as a control design tool; to demonstrate this, we minimize the specific cost of transport of periodic orbits for the compass gait biped, both in the fully actuated and underactuated case

Trajectory tracking and traction coordinating controller design for lunar rover based on dynamics and kinematics analysis

Trajectory tracking control is a necessary part for autonomous navigation of planetary rover and traction coordinating control can reduce the forces consumption during navigation. As a result, a trajectory tracking and traction coordinating controller for wheeled lunar rover with Rocker Bogie is proposed in the paper. Firstly, the longitudinal dynamics model and the kinematics model of six-wheeled rover are established. Secondly, the traction coordinating control algorithm is studied based on sliding mode theory with improved exponential approach law. Thirdly, based on kinematics analysis and traction system identification, the trajectory tracking controller is designed using optimal theory. Then, co-simulations between ADAMS and MATLAB/Simulink are carried out to validate the proposed algorithm, and the simulation results have confirmed the effectiveness of path tracking and traction mobility improving