Dynamically Running Quadrupeds Self-Stable Region Expansion by Mechanical Design

Abstract-Dynamic stability allows running animals to maintain preferred speed during locomotion over rough terrain. It appears that rapid disturbance rejection is an emergent property of the mechanical system. In running robots, simple motor control seems to be effective in the negotiation of rough terrain when used in concert with a mechanical system that stabilizes passively. In this paper, we show that a quadruped robot could be able to perform selfstable running behavior in significantly broader ranges of forward speed and pitch rate with suitable mechanical design. The results presented here are derived by studying the stability of passive dynamics of a quadruped robot running in the sagittal plane in a dimensionless context and can be summarized as: (a) the self-stabilized behavior of a quadruped robot for a particular gait is related to the magnitude of its dimensionless inertia, (b) the values of hip separation, normalized to rest leg length, and the leg relative stiffness of a quadruped robot affect the stability and should be in inverse proportion to its dimensionless inertia, and (c) the self-stable regime of quadruped running robots is enlarged at relatively high forward speeds

Continuum of motion equations and control laws for underactuated mechanical systems

Doctor of PhilosophyDepartment of Mechanical and Nuclear EngineeringYouqi WangWarren N. WhiteAs sizes, lengths, or shapes of a system grow large or shrink to zero, a system will approach limiting forms. As the parameter is allowed to grow or shrink, the system could resemble a simpler system. The sufficient conditions for when the equations of motion will morph from the original system to a target system will be presented. The ball and arc equations of motion morph to those of the ball and beam as the arc’s radius is allowed to grow. The equations of motion for the rotary pendulum, pendubot, and two-link robot manipulator will morph to the equations of motion of the inverted pendulum cart. The effect of a parameter growing large or shrinking to zero has on the controller for the original system will not be fully investigate in this work. A case for when controller morphing might be possible will be examined. A controller for the rotary pendulum will morph to a controller that stabilizes the inverted pendulum cart. Next, a controller for the pendubot will be morphed that does not stabilize the dimensionless inverted pendulum cart. Lastly, a controller for a fully actuated two-link robot manipulator will be morphed to a stabilizing controller for a fully actuated inverted pendulum cart