Research Post

Guaranteed-Safe Approximate Reachability via State Dependency-Based Decomposition


Hamilton Jacobi (HJ) Reachability is a formal verification tool widely used in robotic safety analysis. Given a target set as unsafe states, a dynamical system is guaranteed not to enter the target under the worst-case disturbance if it avoids the Backward Reachable Tube (BRT). However, computing BRTs suffers from exponential computational time and space complexity with respect to the state dimension. Previously, system decomposition and projection techniques have been investigated, but the trade off between applicability to a wider class of dynamics and degree of conservatism has been challenging. In this paper, we propose a State Dependency Graph to represent the system dynamics, and decompose the full system where only dependent states are included in each subsystem, and "missing" states are treated as bounded disturbance. Thus for a large variety of dynamics in robotics, BRTs can be quickly approximated in lower-dimensional chained subsystems with the guaranteed-safety property preserved. We demonstrate our method with numerical experiments on the 4D Quadruple Integrator, and the 6D Bicycle, an important car model that was formerly intractable.

Latest Research Papers

Connect with the community

Get involved in Alberta's growing AI ecosystem! Speaker, sponsorship, and letter of support requests welcome.

Explore training and advanced education

Curious about study options under one of our researchers? Want more information on training opportunities?

Harness the potential of artificial intelligence

Let us know about your goals and challenges for AI adoption in your business. Our Investments & Partnerships team will be in touch shortly!