Spring-Loaded Inverted Pendulum Hopping via Hybrid Averaging and Control Lyapunov Function

The Spring-Loaded Inverted Pendulum(SLIP)has been regarded as a canonical model for hopping and running dynamics of legged robots.This paper presents a novel control of the actuated-SLIP hopping on unknown terrains.We propose that in the neighborhood of the desired stable hybrid limit cycle,the local dynamical behavior of a hybrid system can be expressed by a set of phase coordinates and transverse coordinates.Under some acceptable assumptions,the hybrid averaging theorem is applied on the SLIP non-integrable dynamics to simplify the controller design.Using the inherent symmetry of SLIP dynamics,a control Lyapunov function-based hybrid averaging controller is developed to ensure the exponential stability of the desired gait orbit.This results in a set of linear constraints on the control signal,which can be readily solved by a quadratic programming optimization.Furthermore,a novel method is introduced to improve the robustness against unknown disturbances through the online constraint adjustment.The proposed controller is evaluated in various simulations,demonstrating the SLIP hopping on diverse terrains,including flat,sin-wave,and unregular terrains.The performance of the approach is also validated on a quadruped robot SCIT Dog for generating dynamic gaits such as pronking.

CPG Control for Biped Hopping Robot in Unpredictable Environment

A CPG control mechanism is proposed for hopping motion control of biped robot in unpredictable environment. Based on analysis of robot motion and biological observation of animal＇s control mechanism, the motion control task is divided into two simple parts： motion sequence control and output force control. Inspired by a two-level CPG model, a two-level CPG control mechanism is constructed to coordinate the drivers of robot joint, while various feedback information are introduced into the control mechanism. Interneurons within the control mechanism are modeled to generate motion rhythm and pattern promptly for motion sequence control; motoneurons are modeled to control output forces of joint drivers in real time according to feedbacks. The control system can perceive changes caused by unknown perturbations and environment changes according to feedback information, and adapt to unpredictable environment by adjusting outputs of neurons. The control mechanism is applied to a biped hopping robot in unpredictable environment on simulation platform, and stable adaptive motions are obtained.