Variable Inverted Pendulum Applied to Humanoid Motion Design

Abstract

Double inverted pendulum model, stationary or on a cart, is computationally the simplest out of the range of reasonable models used for anthropomorphic robots motion synthesis. However, it is still not sufficient for describing more complex situations. The novel concept of variable double inverted pendulum (VDIP) for static postures and VDIP on cart (VDIPC) for dynamic cases is proposed. It provides a simplified but a sufficiently accurate tool for planning the human-like static and dynamic robot postures. Its variable parameters enable the description of both human static postures and motion dynamics. The variable length of the lower link is essential for the representation of postures attained by bending legs. The studies of a set of static and dynamic postures were used for deducing and verifying the locations of lower and upper joint of a double pendulum and the point masses. To justify the concept, human body and pendulum behaviors are compared taking into account a typical model of the human body. Static analysis was conducted by considering static human postures. Dynamic conditions were analyzed using the data acquired from human motion and thus the VDIPC definition was established. The zero moment point trajectories of the human and of VDIPC were compared, validating the correctness of VDIPC in dynamic situations. The formal description of VDIPC is provided together with the torques equilibrium condition needed for evaluating the dynamic postural stability, with the VDPIC representing the robot configuration. The VDPIC state equations are formulated in a form required by the predictive control method. The paper contributes to the motion synthesis methods of anthropomorphic robots taking into account postural control.