Hamilton-Jacobi Reachability is a powerful verification tool for robotic systems. However, it is challenging to scale the reachability analysis to the scenarios where multiple agents are operating in the same environment or when a real-time update of the safe set is required, both of which are commonly occurring scenarios in robotics. In this talk, I will discuss how we can alleviate some of these challenges by (a) leveraging the structure in dynamics and control strategy of agents for decoupling the computation of reachable sets, (b) initializing with a previously computed solution and locally updating the reachable set for a faster computation while maintaining safety guarantees, and (c) developing methods that can leverage modern computational tools such as GPUs to improve computation speed by nearly 100 times compared to existing implementations.
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