Conditions for Repetitive Hopping of Semi-Passive Robot Based on Poincaré Map

Abstract

The present paper proposes a method for iterative hopping trajectory generation in a semi-passive robot model (SPR) model and an initial condition according to a slope. The spring-loaded inverted pendulum (SLIP) model has been applied to studies on the trajectories of the walking, running, and jumping of biped or quadruped robots. It is also used in the analysis of movements of animals or implementation of motions in animations. Although the SLIP model in the walking robot field is an effective model with regard to ground reaction force, it cannot control the movement of a spring in real time accurately at a preferred speed. The proposed SPR model is constructed with a structure where two springs are connected in series. One spring is pre-fixed via a constant length in the flight phase. Then, a robot can leap to a higher location as soon as lift-off (LO) occurs using elastic energy due to the ground reaction force during touch-down (TD) in the support phase and energy of the spring compressed by a constant force in the flight phase. A Poincaré map was used to create a hopping trajectory on a slope surface through iterative and constant spring control, and the Newton–Raphson method was employed to search for a fixed point with regard to the iterative hopping cycle. Finally, a fixed point according to various slopes and landing angles was verified through simulations. In general, the speed of the actuator is important for making a robot to jump high. The SPR model has the characteristic of storing energy for jumping in advance at the flight phase. A higher jump can be achieved using a low-speed actuator employing this characteristic. Furthermore, conditions that create an effective trajectory with the limited power of the robot can be calculated based on data in the present paper.