Time-safety trade-offs and a bang-bang algorithm for kinodynamic planning

The kinodynamic planning problem is, given a robot system, to find a trajectory from a start state to a goal state, while avoiding obstacles by a safety margin δ(v) and respecting dynamics bounds. Provably good polynomial-time approximation algorithms for optimal kinodynamic planning find trajectories within ∈ of optimal and have a time complexity polynomial in 1/∈ and in the geometric complexity of the robot world. The authors obtain such algorithms to find near-optimal trajectories obeying piecewise constant extremal controls and bang-bang control. Previous provably good kinodynamic planning algorithms for robot arms produce nonextremal, and hence locally nonoptimal trajectories. Using parameters ∈_T and ∈ _S and describe closeness to optimality in execution time and observance of the safety margin, the authors derive equicomplexity curves to show how their algorithms permit to tradeoffs between time and safety