Discrete-Time Circular Walking Pattern for Biped Robots

When biped robots make turns fast, they may fall due to the action of centrifugal force. This is why one needs to consider the Zero Moment Point (ZMP) equations with respect to cylindrical coordinate system. Those ZMP equations are, however, so coupled and highly nonlinear even for the simple inverted pendulum model that it is hard to find a closed-form solution. Therefore, in this paper, they have been converted through temporal discretization to difference equations that admit numerical solution by most on-board computers. Thus-obtained walking patterns have been characterized and applied to several cases of different speed for comparison purposes. In so doing, the steady patterns have been blended with a type of transitional patterns to change the walking speed in the beginning and/or mid course of walking. Finally, those combined patterns have been put to test on a multi-body robot model by ADAMS (R). Test results show that the robot could walk along a sample circular path as predicted at rapid speeds despite some modeling error, distributed mass and ground contact effects, validating efficacy of the suggested approach.