Hamilton-Jacobi Reachability

Set-valued safety analysis for nonlinear dynamical systems. Each project here computes a reachable set or tube on the joint state space: the answer is not "this trajectory is safe," it is "this entire region of state space admits a control policy that stays safe."

Implemented with helperOC (Mo Chen, UC Berkeley) on top of the level-set library, plus a custom YAPPS-style trajectory-optimisation comparison for the Dubins-airplane case.

Backward reachable tube of a Dubins airplane navigating six cylindrical no-fly pillars

Dubins Airplane Avoidance

BRT computation and HJR feedback for a 4-D Dubins airplane vs. SQP-style trajectory optimisation on a six-pillar benchmark.

Wireless sensor network deployment visualisation with battery-aware routing

Energy-Aware Wireless Networks

Reachability on the joint battery state of a wireless sensor network plus an energy-aware routing layer; ~2× lifetime over shortest-path.

Reduced-order VTOL transition simulation with safety override engaged

VTOL Transition-Mode Envelope

Backward reachable set under worst-case gust disturbance for a planar VTOL; legacy Simulink stability study ported to helperOC.