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This paper presents a dynamic stability analysis method for a trotting quadruped robot on unknown rough terrains, which is based on the Lyapunov theory of a switching system. Firstly, the dynamical model of a trotting quadruped robot is built as a nonlinear switching system. In the stance phase, the dynamical model of a body and two stance legs is approximated as a compound model including a seven-link mechanism and a linear inverted pendulum. Furthermore, as a result of the switching process, the trotting quadruped robot becomes a non-autonomous system. Secondly, a contact force distribution/control strategy is proposed, based on adaptive sliding mode to guarantee the position and orientation of the seven-link mechanism asymptotically stable in the stance phase. With the proposed strategy, a common Lyapunov function is designed in order to validate the uniform asymptotic stability of the body's height and orientation variations. Then, the landing positions of the swing legs are calculated, based on the linear inverted pendulum model in order to make the horizontal position error of the robot converge to a bounded region. Finally, quadruped trotting experiments are performed in order to validate the effectiveness of the proposed methods.

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The two most important performance indicators of quadruped robot are load capacity and walking speed, and these performance indicators of the whole robot finally reflect on the joint torques and angular velocities. To satisfy different requirements of walking speed and load capacity when quadruped robots implement different tasks, the joint torques and angular velocities need to be balanced with physical constraints of the joints. A single leg with redundant DOF (degree of freedom) could optimize the distribution of joint torques or angular velocities based on different performance requirements. This paper presents a kind of new recurrent neural networks taking joint torques and angular velocities simultaneously into consideration and proposes mid-value CLVI-PDNN to achieve the optimal joint torques and angular velocities with physical constraints of the mechanism as described in our previous paper. Because the continuous mid-value CLVI-PDNN has difficulty in real-time operation because of too much calculation workload, two kinds of methods are proposed to discretize the mid-value CLVI-PDNN for application on computer or digital circuit. The simulation results demonstrate the efficacy of the algorithm proposed in this paper.

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