Robotics: Science and Systems XVII

Towards finding the shortest-paths for 3D rigid bodies

Weifu Wang, Ping Li


In this work; we analyze and present an algorithm to find shortest-paths for generic rigid bodies. We derived the necessary conditions for optimality using Lagrange multipliers; and compared it to the conditions derived from Pontraygin's Maximum Principle. We derived the equations of the necessary conditions using geometric Jacobian; drawing inspiration from the similarity between the rigid-body systems and the arm-like systems. In the previous work, the analysis focused on finding shortest-paths to reach goals in positions only. This work extends the analysis to find the shortest-path to reach a goal with complete configuration in 3D. We show that the algorithm is resolution complete even when the orientations are included. To overcome the complexity of 3D orientations; we describe the system using three points in the robot frame; and show that this parameter system is redundant but can derive the same necessary conditions as those derived using the minimum parameters (configuration). We used a 3D Dubins system to demonstrate the correctness of the analysis and the algorithm.



    AUTHOR    = {Weifu Wang AND Ping Li}, 
    TITLE     = {{Towards finding the shortest-paths for 3D rigid bodies}}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2021}, 
    ADDRESS   = {Virtual}, 
    MONTH     = {July}, 
    DOI       = {10.15607/RSS.2021.XVII.085}