Endogenous Configuration Space Approach: An Intersection of Robotics and Control Theory

Abstract

The endogenous configuration space approach is a control theory-oriented methodology of robotics research, dedicated to mobile manipulators. A cornerstone of the approach is a parameterized control system with output whose input–output map constitutes the mobile manipulator’s kinematics. An endogenous configuration consists of the control function and of the vector of output function parameters representing the joint positions of the on-board manipulator. The mobile manipulator’s Jacobian is defined as the input–output map of the linear approximation to the control system. Regular and singular endogenous configurations are introduced. The regular endogenous configuration corresponds to the local output controllability of the control system, while the singular configuration coincides with a singular optimal control-parameter pair of the control system. The inverse kinematics problem is formulated as a control problem in a driftless control system. A collection of Jacobian kinematics inverses is presented, leading to Jacobian motion planning algorithms. Performance measures of the mobile manipulator are introduced.