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This paper introduces AkinoPDF, a novel parallelized sampling-based kinodynamic motion planning technique leveraging differential flatness to drastically reduce computation time for high-DOF robots. By transforming the planning problem into a flat output space, AkinoPDF enables analytical solutions for BVPs and dynamics integration, allowing for rapid generation of dynamically feasible trajectories. Experimental results demonstrate planning times in the microsecond to millisecond range in complex environments, showcasing a significant speedup compared to traditional kinodynamic planners.
Kinodynamic motion planning just got a whole lot faster: AkinoPDF achieves microsecond-level planning times by exploiting differential flatness for analytical solutions.
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.
