Sampling-based Algorithms for Optimal Motion Planning Using Closed-loop Prediction

Motion planning under differential constraints, kinodynamic motion planning, is one of the canonical problems in robotics. Currently, state-of-the-art methods evolve around kinodynamic variants of popular sampling-based algorithms, such as Rapidly-exploring Random Trees (RRTs). However, there are still challenges remaining, for example, how to include complex dynamics while guaranteeing optimality. If the open-loop dynamics are unstable, exploration by random sampling in control space becomes inefficient. We describe a new sampling-based algorithm, called CL-RRT#, which leverages ideas from the RRT# algorithm and a variant of the RRT algorithm that generates trajectories using closed-loop prediction. The idea of planning with closed-loop prediction allows us to handle complex unstable dynamics and avoids the need to find computationally hard steering procedures. The search technique presented in the RRT# algorithm allows us to improve the solution quality by searching over alternative reference trajectories. Numerical simulations using a nonholonomic system demonstrate the benefits of the proposed approach.