A Differential Dynamic Programming-based Approach for Balancing Energy and Time Optimality in Motion Planning

Optimal motion planning that simultaneously considers energy and time efficiency is crucial for a wide range of applications from industrial manufacturing to autonomous vehicle navigation. This paper introduces a novel perspective on discrete-time systems which recognizes the time interval size as an additional aspect of the control variable that is conventionally sought to be determined. By incorporating ideas from Dynamic Differential Programming (DDP), our method, called BO-DDP (Balancing energy and time Optimality via DDP), enables an adjustable trade-off between energy and time optimality. DDP leverages quadratic approximation of dynamics and cost function, ensuring accurate information capture and a high convergence rate. To address the challenge of high computational complexity in obtaining related derivatives, we introduce a Taylor series-based numerical scheme for simultaneous forward integration and differentiation. Extensive simulation experiments on two scenarios, including autonomous car navigation and quadcopter flight, demonstrate the practicality and effectiveness of our algorithm.