New Math Keeps Self-Driving Cars Safer in Crowded Traffic

Researchers Amirsaeid Safari and Jesse B. Hoagg introduce predicted-flow control barrier functions (P-CBFs) for non-control-affine systems. Control barrier functions (CBFs) enforce safety through conditions imposed pointwise in time without consideration of state evolution over a future horizon, which makes CBF-based controls typically myopic. P-CBFs generalize CBFs from a function of the current state to a functional of the predicted flow under a parametrized control, so they can certify safety over the entire prediction horizon while simultaneously allowing performance optimization over that horizon. But prior work with P-CBFs only applied to control-affine systems and suffered from a limitation where the prediction horizon could shrink or even vanish. The article addresses both shortcomings by introducing a planning control that smoothly transitions from a parametric plan to a backup control (if needed) and a time-shift parameter that determines if a transition is needed. The evolution of the control-plan and time-shift parameters is determined from a single guaranteed-feasible convex optimization, which reduces to a quadratic program if the control limits are a convex polyhedron, and the real-time executed control is determined from the instantaneous planning control and time shift. This method simultaneously addresses safety certification and performance optimization over the fixed prediction horizon. The approach is compared to