Real-Time Generation of Formal Dynamic Bounding-Boxes with Density Distribution for Automated Driving

A computer that includes a processor and a memory can determine a final trajectory for a vehicle by determining a candidate trajectory of a first object based on a detected second object. The candidate trajectory can be input to a reachable polyhedral marching processor to determine dynamic occupancy polyhedrals based on a shape of the candidate trajectory. A reachable tube can be determined based on combining the dynamic occupancy polyhedrals and the final trajectory can be determined based on the reachable tube avoiding the detected second object.