Ultrafast Sampling-based Kinodynamic Planning via Differential Flatness

Motion planning under dynamics constraints, i.e., kinodynamic planning, enables safe robot operation by generating dynamically feasible trajectories that the robot can accurately track. For high-\dof robots such as manipulators, sampling-based motion planners are commonly used, especially for complex tasks in cluttered environments. However, enforcing constraints on robot dynamics in such planners requires solving either challenging two-point boundary value problems (BVPs) or propagating robot dynamics over time, both of which are computational bottlenecks that drastically increase planning times. Meanwhile, recent efforts have shown that sampling-based motion planners can generate plans in microseconds using parallelization, but are limited to geometric paths. This paper develops AkinoPDF, a fast parallelized sampling-based kinodynamic motion planning technique for a broad class of differentially flat robot systems, including manipulators, ground and aerial vehicles, and more. Differential flatness allows us to transform the motion planning problem from the original state space to a flat output space, where an analytical time-parameterized solution of the BVP and dynamics integration can be obtained. A trajectory in the flat output space is then converted back to a closed-form dynamically feasible trajectory in the original state space, enabling fast validation via ``single instruction, multiple data" parallelism. Our method is fast, exact, and compatible with any sampling-based motion planner. We extensively verify the effectiveness of our approach in both simulated benchmarks and real experiments with cluttered and dynamic environments, requiring mere microseconds to milliseconds of planning time.

Collision-Affording Point Trees: SIMD-Amenable Nearest Neighbors for Fast Collision Checking

Motion planning against sensor data is often a critical bottleneck in real-time robot control. For sampling-based motion planners, which are effective for high-dimensional systems such as manipulators, the most time-intensive component is collision checking. We present a novel spatial data structure, the collision-affording point tree (CAPT): an exact representation of point clouds that accelerates collision-checking queries between robots and point clouds by an order of magnitude, with an average query time of less than 10 nanoseconds on 3D scenes comprising thousands of points. With the CAPT, sampling-based planners can generate valid, high-quality paths in under a millisecond, with total end-to-end computation time faster than 60 FPS, on a single thread of a consumer-grade CPU. We also present a point cloud filtering algorithm, based on space-filling curves, which reduces the number of points in a point cloud while preserving structure. Our approach enables robots to plan at real-time speeds in sensed environments, opening up potential uses of planning for high-dimensional systems in dynamic, changing, and unmodeled environments.