This paper develops nonholonomic motion planning strategy for three-joint underactuated manipulator, which uses only two\nactuators and can be converted into chained form. Since themanipulator was designed focusing on the control simplicity, there are\nseveral issues for motion planning, mainly including transformation singularity, path estimation, and trajectory robustness in the\npresence of initial errors, which need to be considered. Although many existing motion planning control laws for chained form\nsystem can be directly applied to themanipulator and steer it to desired configuration, coordinate transformation singularities often\nhappen. We propose two mathematical techniques to avoid the transformation singularities. Then, two evaluation indicators are\ndefined and used to estimate control precision and linear approximation capability. In the end, the initial error sensitivity matrix is\nintroduced to describe the interference sensitivity, which is called robustness. The simulation and experimental results show that\nan efficient and robust resultant path of three-joint underactuated manipulator can be successfully obtained by use of the motion\nplanning strategy we presented.
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