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… Click to show full abstract
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.
               
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