Captivity-Escape Games as a Means for Safety in Online Motion Generation

Sampling-Based Model-Predictive Control (MPC) algorithms are a flexible class of controllers used for navigation on a wide range of robotic systems. Historically, such approaches have lacked hard safety guarantees, a shortcoming which we remedy in this work by computing guaranteed reachable-set overapproximations online with a fast, interval-based pipeline. We show that our method achieves similar performance to a state-of-the-art reachability-based planner without the need for the expensive pre-computation step, and can be scaled to systems that are infeasible using existing approaches. Finally, we demonstrate that our technique reduces safety violations by over 99% in a racing simulation and successfully controls a model racecar on real hardware experiments without crashes.

We present GASP, a GPU-Accelerated Safe Planner for real-time, collision-aware joint-space motion generation in known environments. GASP combines a clamped B-spline trajectory parameterization with a convolutional residual neural network that predicts the free interior control points, while analytically inserted boundary control points enforce initial and final derivative constraints for collision-aware planning under non-stationary conditions. A conditional variational autoencoder samples multiple trajectory candidates, which are decoded and validated in parallel on the GPU, yielding a batched planner for collision-aware coupled joint-space motion with near-millisecond inference. We validate GASP as an online motion-generation module, where it achieves analytical-level success rates with high collision-aware feasibility and substantially reduces inference time relative to GPU-based trajectory optimization. We further deploy GASP as a reinforcement-learning reset planner in competitive robotic table tennis, matching the baseline return rate while roughly halving training-time collisions.

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.