GASP: GPU-Accelerated Safe Planner for Real-Time Collision-Aware Motion Generation with Latent Trajectory Sampling

Reactive motion generation in unstructured environments remains an open challenge in robotics. Due to the computational complexity of collision-free motion generation, existing methods either generate global trajectories for static scenarios, or employ models that make conservative assumptions about the environment. This paper identifies the primary bottleneck as the runtime performance demand of planning on high-fidelity environments, and the temporal integration between the perception and planning modules. Therefore, we propose a framework that does not compromise on runtime performance and world representations for perception and planning by accelerating world modeling and vector-field based planning using the GPU. This allows us to achieve faster parallel state exploration for quasi-global trajectory planning, and tighter coupling of the perception-action loop in real-time for dynamic cluttered environments with off-the-shelf depth sensors. We quantitatively evaluate the computation-time and success rate differences for the CPU and GPU versions of our planner, and perform qualitative evaluations of our coupled framework using real-world experiments on a 7-DoF Franka Emika robot. Experimental results demonstrate that our GPU-based framework achieves up to a 5x speedup over the CPU version and successfully avoids collisions across both trivial and challenging physical world scenarios.

In this paper, we present an online method for converting an arbitrary geometric path, represented by a sequence of states, and generated by any planner (e.g., sampling-based planners such as RRT or PRM, search-based planners such as ARA*, etc.), into a kinematically feasible, jerk-limited trajectory. The method generates a sequence of quintic/quartic splines that can be discretized at a user-specified control rate and streamed to a low-level robot controller. Our approach enables real-time adaptation to environmental changes and can be re-invoked at any instant to generate a new trajectory from the robot's current state to a desired target state or sequence of states. Under a bounded-obstacle-velocity assumption, the method provides conditional stopping-safety guarantees over a finite time interval in dynamic environments, while allowing bounded geometric deviation from the original path. Kinematic constraints, including jerk limits, are explicitly considered. We validate the approach in a comparative simulation study against a competing method, demonstrating favorable behavior w.r.t. smoothness, computational time, and real-time performance, particularly with frequent target-state changes (up to 1 [kHz]). Real-robot experiments demonstrate applicability in real-world scenarios, including scenarios with a human as an obstacle.

Planners on graphs of convex sets return trajectories that are collision-free by construction, provided the convex regions are collision-free. The region generator only promises that property probabilistically, and no planner in the family verifies it. We report the first measurement of what the gap costs. On a scaled 14-DOF bimanual library, $3.2\%$ of interface samples are in collision, and a search-based GCS planner (\gcsstar) turns that volume error into a $62\%$ answer error: $18$ of $29$ pick-and-place queries return trajectories that drive the arms through the shelves, up to $91$,mm deep, reported as successes. Repairing the library does not work; a ten times stricter acceptance contract, sums-of-squares certified regions, and uniform margins each destroy the connectivity planning needs before they deliver soundness. We instead build a planner that certifies its answers. It samples the overlaps and shared faces of the decomposition, prunes with an admissible informed bound, and verifies the one candidate each search round proposes, continuously, by a chain of clearance certificate balls with no resolution parameter; failures are repaired with local in-region detours, and the convex polish is re-verified. Head-to-head on all $29$ task queries it delivers zero invalid answers against $21$ for the reference, reaches its first certified answer in $0.11$,s against $1.59$,s for the reference's unverified one, and reproduces the reference optimum exactly on every query whose reference answer is physically valid.