The Multi-Appendage Robotic System (MARS) is a hexapedal robotic platform capable of walking and of performing manipulation tasks. Each of the six limbs of MARS incorporates a three-degree of freedom (DOF), kinematically spherical proximal joint, similar to a shoulder or hip joint, and a 1-DOF distal joint, similar to an elbow or knee joint. The generation of walking gaits for such robots with multiple limbs requires a thorough understanding of the kinematics of the limbs, including their workspace. Since the entire limb workspace cannot be used in a statically stable alternating tripedal gait for such a robot, a subset of the general limb workspace is defined to be used for walking gait generation algorithms. The specific abilities of a walking algorithm dictate the usable workspace for the limbs. Generally speaking, the more general the walking algorithm is, the less constricted the workspace becomes. In this paper we develop the workspaces for the limb of MARS in the knee up configuration, which range from simple 2D geometry to complex 3D volume, and analyze its limitations for use in walking on flat level surfaces. Next we discuss the case when the robot body is not parallel to the ground. The results from this paper can be applied to the development of walking gait generation algorithms.

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