A Real-Time Approach for Chance-Constrained Motion Planning with Dynamic Obstacles

Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on optimal motion planning has employed two main strategies to define a safe bound on an obstacle's space: using a polyhedron or a nonlinear differentiable surface. The former approach relies on disjunctive programming, which has a relatively high computational cost that grows exponentially with the number of obstacles. The latter approach needs to be linearized locally to find a tractable evaluation of the chance constraints, which dramatically reduces the remaining free space and leads to over-conservative trajectories or even unfeasibility. In this work, we present a hybrid approach that eludes the pitfalls of both strategies while maintaining the original safety guarantees. The key idea consists in obtaining a safe differentiable approximation for the disjunctive chance constraints bounding the obstacles. The resulting nonlinear optimization problem can be efficiently solved to meet fast real-time requirements with multiple obstacles. We validate our approach through mathematical proof, simulation and real experiments with an aerial robot using nonlinear model predictive control to avoid pedestrians.