We address the motion planning problem for a robotic system whose configuration manifold contains a group of rotations. Our approach is applied to a free-floating space robot composed of a three-dimensional base (a spacecraft) and an anthropomorphic onboard manipulator. The robot is actuated by the torques exerted at the joints of the onboard manipulator. A coordinate-free representation of rotations is utilized. The Lagrangian formalism is employed in order to derive a dynamics model of the robot that takes the form of a control system defined on the group of rotations and the joint space of the onboard manipulator. Using the conservation of angular momentum of the robot, a Jacobian motion planning algorithm is designed relying on the Endogenous Configuration Space Approach. The performance of the algorithm is verified by computer simulations.

This paper discusses the nonholonomic robotic systems whose motion constraints assume the Pfaffian form, and the equations of motion are represented by driftless control systems with outputs. By reference to the end point map of such a control system, we define the system's Jacobian and study Jacobian motion-planning algorithms. A new Lagrange-type Jacobian inverse, referred to as the General Lagrangian Jacobian Inverse (GLJI), is designed as the solution of an optimal control problem with a Lagrange-type objective function. Singularities of GLJI are examined. A special choice of the objective function illustrates features of GLJI. A new motion-planning algorithm based on GLJI is proposed. Theoretical arguments are illustrated with a motion-planning problem of a space robot.