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We present an efficient approach to generating paths for humanoids and other robotic manipulators that uses the Task Space Region (TSR) framework to specify manipulation tasks. TSRs can define acceptable goal poses of an end-effector or constraints on the end-effector's pose during the path, or both. First presented as a method for goal-specification, TSRs are a straightforward representation of sets of end-effector poses which can be sampled and which entail a clear distance metric. This makes TSRs ideal for sampling-based motion planning. However, a finite set of TSRs is sometimes insufficient to capture the pose constraints of a given task. To describe more complex constraints, we present TSR Chains, which are defined by linking a series of TSRs. Though the sampling for TSR Chains follows clearly from that of TSRs, the distance metric for TSR Chains is radically different. We also present a new version of our Constrained Bidirectional RRT (CBiRRT2) planner, which is capable of planning with TSR chains as well as other constraints. We demonstrate our approach on the HRP3 robot by performing a variety of whole-body manipulation tasks.