Our research is mainly concerned with the path planning problem with general end-eflector constraints (PPGEC) for robot manipulators with many degrees of freedom. For example, a robot manipulator holding a glass of water should keep the glass vertically up all the time, a constraint on end-effector orientation; or, in some other cases, the end-effector may be constrained to move in a plane, a constraint on end-effector position. In this thesis, we show that there are two approaches to deal with the PPGEC problem. The first approach is adapted from the existing randomized gradient descent method  for closed-chain robots. The second approach is a new planning algorithm called ATACE, Alternate Task-space And C-space Exploration. Unlike the first approach which works only in the configuration space, ATACE works in both the task space and the configuration space. Instead of finding a path in the configuration space directly, ATACE finds an end-effector path in the task space, and then computes the corresponding configuration space path by tracking this end-effector path. In our simulation environment, we have implemented and compared these two a p proaches. With intuitive explanations, we outline scenarios where one planner is better than the other.
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