Lifted Newton motion planning algorithm

This paper presents an application of the Lifted Newton method in the motion planning of robotics systems represented by a nonlinear control system with output. This representation covers a wide range of systems, from simple nonholonomic systems modeled on kinematics level to complex systems with dynamics. Following the Endogenous Configuration Space Approach, the motion planning problem is defined in terms of the system end-point map that transforms input control signals into task space location at a prescribed time. The Lifted Newton method is a generalization of the well-known direct “multiple shooting” techniques, originally applied to solving nonlinear optimization problems, including the optimal control problem and the optimal estimation problem as well as to solving boundary value problems. Compared to traditional Newton-type algorithms, typically the Lifted Newton method has larger region of convergence, faster local convergence rate and more freedom for initialization. It has also a ability for remarkable parallelization of the most computational demanding algorithm parts. Performance of the algorithm has been illustrated by solving a motion planning problem for the unicycle type platform and the rolling ball.