Design for energy loss and energy control in a galloping artificial quadruped
This thesis describes a set of models and design requirements which facilitate the design of a quadrupedal machine capable of gallop gaits. Quadruped design begins with the design of the legs. A spring-mass inverted pendulum model is very simple and has been shown to describe legged locomotion energetics. A five rigid body model is also considered, but offers only marginal improvement in fidelity for an immense increase in complexity. The spring-mass inverted pendulum model is used to generate approximate relationships between model parameters and gait parameters for lossless, steady-state gaits. These relationships are generated by running thousands of simulations over a range of carefully chosen initial conditions. The relationships are all chosen to satisfy ‘Raibert symmetry’, a set of conditions which describe a lossless idealized modulo one gait. These simulation results are grouped into dimensionless groups via the Buckingham Pi theorem. Coefficients for three approximating polynomials are chosen using conventional regression techniques. These three approximating polynomials can be used to investigate design implications including surface friction requirements for a given speed and structural requirements. A set of design requirements is outlined. The KOLT (OSU/Stanford artificial quadruped) leg design is described. To model the quadruped, an impulse can be used to model leg-ground interactions, a rigid body can be used to model the quadruped and an impulsive moment can be used to model neck and back flexion. This impulse model can generate all quadrupedal gaits, including the gallop gaits, and has a simple analytic solution. These gallop gait solutions suggests that the forces exerted by biological quadrupeds on the ground may not act exactly along the axis of the legs. The impulse model can be used to predict lateral and vertical impulse magnitudes, the effect of leg location changes and the effect of stance torques. A set of design requirements for the KOLT is outlined. The KOLT design is described. The impulse model is used to derive a nonlinear plant model for control around a stable gait pattern. The plant model can be linearized if certain assumptions are met.