A Reachability-Based Spatio-Temporal Sampling Strategy for Kinodynamic Motion Planning

Abstract

By limiting the planning domain to “ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Informed Set”, some sampling-based motion planners (SBMP) (e.g., Informed RRT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> , BIT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sup> ) can solve the geometric motion planning problems efficiently. However, the construction of informed set (IS) will be very challenging, when further differential constraints are considered. For the time-optimal kinodynamic motion planning problem, this paper defines a modified time informed set (MTIS) to limit the planning domain. Due to drawing inspiration from Hamilton-Jacobi-Bellman (HJB) reachability analysis, MTIS, compared with the original TIS, can not only help save the running time of SBMP, but also extend the applicable scope from linear systems to polynomial nonlinear systems with control constrains. On this basis, a spatio-temporal sampling strategy adapted to MTIS is proposed. Firstly, MTIS is used to estimate the optimal cost and the valid tree structure is reused, so that we do not need to provide a solution trajectory in advance. Secondly, this strategy is generic, allowing it to be combined with common SBMP (such as SST, etc.) to accelerate convergence and reduce the memory requirement. Several simulation experiments also demonstrate the effectiveness of proposed method.