Motion control of a planar nonholonomic system with four DoF is addressed in this paper. Three actuators are responsible for shape control of this system. Furthermore, assuming no external forces and zero angular momentum, imposes a nonholonomic constraint to the problem. First it is shown that although the simplified equations of motion for this system, could be converted to Heisenberg and chained-form systems, the conventional control methods for these systems, may not be applied to the considered problem. Then, using sliding modes and online path planning, two different closed-loop control laws are designed for bringing the system to and stabilizing around any desired equilibrium state started from any initial condition. Simulation results, show the efficiency of the proposed methods.

Keywords: Tethered Satellites, Nonholonomic Constraint, Control, Shape Change

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