This paper discusses a modification of the Newton algorithm applied to nonholonomic motion planning with energy optimization. The energy optimization is performed either by optimizing motion in the null space of the Jacobian matrix derived from the nonholonomic system or coupling this motion with movement toward the goal. Resulting controls are smooth and easily generated by motors or thrusters. The two methods can be used, when kinematics are considered, to steer any driftless nonholonomic systems particular free-floating objects, underactuated manipulators, mobile robots (with trailers). Similarities and differences are also discussed in the Newton algorithm for holonomic and nonholonomic systems.

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Keywords Algorithms, Motion-planning, Optimal control, Robots
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Journal IEEE Transactions on Control Systems Technology
Duleba, I. (Ignacy), & Sasiadek, J. (2003). Nonholonomic motion planning based on Newton algorithm with energy optimization. IEEE Transactions on Control Systems Technology, 11(3), 355–363. doi:10.1109/TCST.2003.810394