A Rigorous Optimization Approach for the Generic Derivation of Secondary Information from Digital Maps for Urban Scenarios

In the context of Highly Automated Driving (HAD) and Advanced Driver Assistance Systems (ADAS), we derive optimal stopping points for vehicles in urban scenarios. We develop a rigorous global optimization algorithm and apply it to a constrained maximization problem that is based on a high-definition map (HD map). Specific map feature functions describe the contribution of the points, curves, and polygons to the urban scenario model, while the perceived obstacles form infeasible areas. Our algorithm combines a branch-and-bound method using interval arithmetic with locally applied cubic Taylor expansions of the objective function. The polynomial maximization problem with box constraints is formulated as a root finding problem that we solve using an eigenvalue approach. We test the developed algorithm in urban scenarios and compare it to interval algorithms that either use local quadratic Taylor approaches or no local improvement at all.