Whole Body Planning of Mobile Manipulators Leveraging Lie Theory based Optimization

William Smith, Siddharth Singh, Julia Rudy, Yuxiang Guan

Keywords: mobile manipulation, lie theory, optimization, trajectory planning, motion planning

TL;DR: We propose a method for whole body motion planning of mobile manipulators using Lie theory and constrained optimization to generate the proper states from inverse kinematics.

Abstract: Mobile manipulators find use in several applications in distinct setups. The current issues with mobile manipulation are the large state space provided by the mobile base and the challenge of modeling high degree of freedom systems. In this work, we propose a Lie theory and optimization based approach for whole body planning of mobile manipulators to address these issues. Existing kinematics based approaches are unable to converge to an optimized joint state due to a seemingly infinite state space provided by the unconstrained motion of the base. We propose using a Lie theory based optimization framework to find the inverse kinematic constraints by converting the kinematic model, created using screw coordinates, between its Lie group and vector representation. An optimization function is devised to solve for the desired joint states of the entire mobile manipulator while including collision check constraints. This allows the motion of the mobile base and manipulator to be planned and applied in unison. The optimization framework also allows other desired conditions to be considered without large changes to the structure of the method. The performance of the whole body state planner is validated on multiple mobile manipulators in simulation with both the holonomic and non-holonomic mobile bases.

Submission Number: 19