Sampled-Data Hamilton-Jacobi Reachability Based Safe Motion Planning In Dynamic Environments

Generating safe motions to perform tasks under uncertain conditions is a major challenge posed by the increasing integration of robotic systems into our daily life,but traditional robust Motion Planning(MP)methods usually fail to ensure robust safety and performance.Besides,reachability analysis provides powerful tools for the safety verication of state-constrained control systems under uncertainty,but has seldomly been applied to robust MP problems.In this thesis we develop a formal and systematic approach based on reachability analysis to achieve robust MP in dynamic environments under uncertainty.Firstly,we solve the robust MP problem in static environments.The motion plan is computed oine by the Sampled-Data(SD)Hamilton-Jacobi(HJ)reachability algorithm,a recursive method breaking down the problem into a sequence of dierential games.Online,a provably robust safety-preserving and target-reaching feedback control is synthesized.Secondly,we extend this algorithm to time-varying environments by augmenting the state with a time dimension.Thirdly,the case of adversarial environments is handled by reasoning in a higher dimensional joint state space.Furthermore,we prove that the curse of dimensionality can be signicantly mitigated by performing specic projections onto lower dimensional subspaces without threatening any guarantees.Fourthly,the case of non-point robots is discussed by transposing the previous algorithms into the conguration space.The validity and eciency of our approach are continuously demonstrated throughout this thesis by the means of example cases.Our validation culminates with the study of a robot arm subject to measurement errors that is tasked with reaching a moving target while avoiding collision with moving obstacles and capture by an unpredictable pursuer.This last simulation experiment combines all the aspects previously explored into the same scenario and thus conrms that our methodology is ecient,generic and exible.Finally,perspectives of future research on reachability-based robust MP methods are thoroughly discussed.