Investigation of an Articulated Spine in a Quadruped Robotic System.

This research quantitatively analyzes a multi-body dynamics quadrupedal model with an articulated spine to evaluate the effects of speed and stride frequency on the energy requirements of the system. The articulated model consists of six planar, rigid bodies with a single joint in the middle of the torso. All joints are frictionless and mass is equally distributed in the limbs and torso. A model with the mid-torso joint removed, denoted as the rigid model, is used as a baseline comparison. Impulsive forces and torques are used to instantaneously reset the velocities at the phase transitions, allowing for ballistic trajectories during flight phases. Active torques at the haunch and shoulder joints are used during the stance phases to increase the model robustness. Simulations were conducted over effective high-speed gaits from 6.0 - 9.0 m/s. Stride frequencies were varied for both models. An evolutionary algorithm was employed to find plausible gaits based on biologically realistic constraints and bounds. The objective function for the optimization was cost of transport. Results show a decreasing cost of transport as speed increases for the articulated model with an optimal stride frequency of 3 s$^{-1}$ and an increasing cost of transport with increasing speed for the rigid model at an optimal stride frequency of 1.4 s$^{-1}$, with a crossover in the cost of transport between the two models occurring at 7.0 m/s. The rigid model favors low speeds and stride frequencies at the cost of a large impulsive vertical force, driving the system through a long, gathered flight phase used to cover the long distances at the low stride frequencies. The articulated model prefers higher speeds and stride frequencies at the cost of a large impulsive torque in the back joint, akin to the contraction of abdomen muscles, preventing the collapse of the back. Thus, it is demonstrated that the inclusion of back articulation enables a more energetically efficient high-speed gait than a rigid back system, as seen in biological systems. Detailed analysis is provided to identify the mechanics associated with the optimal gaits of both the rigid and the articulated systems to support this claim.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89831/1/bhaueise_1.pd

Energetics and Passive Dynamics of Quadruped Robot Planar Running Gaits

Quadruped robots find application in military for load carrying over uneven terrain, humanitarian de-mining, and search and rescue missions. The energy required for quadruped robot locomotion needs to be supplied from on-board energy source which can be either electrical batteries or fuels such as gasolene/diesel. The range and duration of missions very much depend on the amount of energy carried, which is highly limited. Hence, energy efficiency is of paramount importance in building quadruped robots. Study of energy efficiency in quadruped robots not only helps in efficient design of quadruped robots, but also helps understand the biomechanics of quadrupedal animals. This thesis focuses on the energy efficiency of planar running gaits and presents: (a) derivation of cost of transport expressions for trot and bounding gaits, (b) advantages of articulated torso over rigid torso for quadruped robot, (c) symmetry based control laws for passive dynamic bounding and design for inherent stability, and (d) effect of asymmetry in zero-energy bounding gaits