SUMMARYWe propose a novel formal approach to robust motion planning (MP) in dynamic environments based on reachability analysis. While traditional MP methods usually fail to provide formal robust safety and performance guarantees, our approach provably ensures safe task achievement in time-varying and adversarial environments under parametric uncertainty. We leverage recent results on Hamilton–Jacobi (HJ) reachability and differential games in order to compute offline guaranteed motion plans that are compatible with the sampled-data (SD) paradigm. Also, we synthesize online provably robust safety-preserving and target-reaching feedback controls. Unlike earlier applications of reachability analysis to MP, our methodology handles arbitrary time-varying constraints, adversarial agents such as pursuing obstacles or evading targets, and takes into account the robot’s configuration. Furthermore, we use HJ projections in order to reduce significantly the computational burden without trading off safety guarantees. The validity of this approach is demonstrated through the case study of a robot arm subject to measurement errors, which is tasked with safely reaching a goal in a known time-varying workspace while avoiding capture by an unpredictable pursuer. Finally, the performance of the approach and research perspectives are discussed.