The Multi-Appendage Robotic System (MARS) built for this research is a hexapod robotic platform capable of walking and 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. Designing walking gaits for such multi-limb robots requires a thorough understanding of the kinematics of the limbs, including their workspace. The specic 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. However, the entire limb workspace cannot be used in a continuous, statically stable, alternating tripedal gait for such a robot; therefore a subset of the limb workspace is dened for walking algorithms. This thesis develops MARS limb workspaces in the knee up conguration, and analyzes its limitations for walking on planar surfaces. The workspaces range from simple 2D geometry to complex 3D volumes. While MARS is a hexapedal robot, the tasks of dening the workspace and walking agorthm for all six limbs can be abstracted to a single limb using the constraint of a tripedal, statically stable gait. Based on understanding the behavior of an individual limb, a walking algorithm was developed to allow MARS to walk on level terrain. The algorithm is adaptive in that it continously updates based on control inputs. Open Tech developed a similar algorithm, based on a 2D workspace. This simpler algorithm developed resulted in smooth gait generation, with near-instantaneous response to control input. This accomplishment demonstrated the feasibility of implementing a more sophisticated algorithm, allowing for inputs of all six DOF: x and y velocity, z velocity or walking height, yaw, pitch and roll. This latter algorithm uses a 3D workspace developed to aord near-maximum step length. The workspace analysis and walking algorithm development in this thesis can be applied to the further advancement of walking gait generation algorithms. / Master of Science