SCRAMPPI: Contingency-Constrained Planning using Hamilton-Jacobi Reachability

Autonomous robots commonly aim to achieve a nominal objective while minimizing a cost. Without contingency preparation, this can leave them vulnerable to mission failure. This is formalized as a trajectory optimization problem over the nominal cost with a contingency constraint: from each checked state along the nominal plan, an admissible contingency maneuver must exist that reaches a designated recovery target within a prescribed contingency horizon. Existing methods either optimize contingency trajectories alongside the nominal plan or evaluate this constraint through computationally expensive nested sampling-based searches. Instead, we introduce SCRAMPPI, which represents this requirement as a reach-avoid problem and leverages Hamilton--Jacobi (HJ) reachability analysis to evaluate contingency feasibility. By either computing a reach-avoid value function offline or updating it only as the environment is revealed, and integrating it with model predictive path integral (MPPI) control via resampling-based rollouts, SCRAMPPI provides contingency-feasibility evaluations while still planning in 15-20 hz. Finally, we present simulated and hardware experiments demonstrating real-time nominal planning and execution of contingency maneuvers in mobile-robot navigation, alongside a five-dimensional friction-limited recovery simulation.