Towards Fast Safe Mission Planning

Robotic and cyber-physical systems are proliferating at a breakneck pace. A key technological hurdle is to ensure safety of such systems especially within proximity of humans. While there has been a push in identifying obstacles and unsafe situations via sensors and machine learned predictors, the task of embedding such information to determine safe course while obeying rules-of-the-road is non-trivial. Further, the uncertainty and noise in prediction together with near real-time requirements under bounded computation resources makes this problem very challenging. This work proposes an architecture for fast, safe planning of autonomous missions. We build upon the recent work in Probabilistic Signal Temporal Logic (PrSTL) that synthesizes provably safe controllers that take into account noisy sensors and associated uncertainty in learned classifier/regressor predictions. Currently, solution for PrSTL requires solving Mixed Integer Semi-Definite Programs (MISDPs), which quickly become infeasible to solve in reasonable time as the number of constraints grow. Further, PrSTL needs the description of the mission goal and the required safety invariants as logical formulations and often expressing such objectives and constraints for long horizons and complicated rules-of-the-road remain non-trivial at best. We alleviate these problems by combining PrSTL with random sampling based planners. We propose using Rapidly-exploring Random Trees (RRT) and associated variants like RRT* to simplify computation by first efficiently sampling feasible points in the robot’s configuration space and then generating trajectories by connecting them via safe control. Such fast sampling of the feasible trajectories effectively reduces the optimization from a MISDP to a sequence of Second Order Cone Programs (SOCP), which being convex, can be solved much more efficiently.