In this dissertation, a mathematical model is developed for a quadruped walking robot to investigate the dynamic stability considering all the inertial effects in the system including those of legs. The dynamic model is derived based on Lagrange's equation using matrix-vector notations for the simpler expression, also the foot strike phenomenon is taken into consideration modeling the foot strike as collision between the terrain surface and the landing foot.
And an instant gait stability measure is proposed to apply to dynamic gaits as well as static gaits. The gait stability measure is obtained from the angular momentum of the system about the supporting edges also considering the effect of the swing legs. Some novel parameters, such as the reference angular momentum $H^{ref}_l$ and the maximum angular momentum $H^{max}_l$ are defined to obtain the gait stability measure about each edge in the support polygon. The validity of the gait stability measure is examined along with the gait stability analysis for several representative gait parameters using the developed dynamic model. The proposed gait stability measure can be utilized in designing the optimal trajectory of the quadrupedal walking gaits and also be extended to other multi-legged walking robots such as hexapod walking robots.
Then the foot strike preparation scheme is proposed introducing the foot strike preparatory time factor γ to improve the stability of the dynamic gaits and its effectiveness is verified using the numerical simulations and the gait experiment with the quadruped walking robot CENTAUR.
