Seeking the Analytical Approximation of the Stance Dynamics of the 3D SpringLoaded Inverted Pendulum Model By Using Perturbation Approach The SpringLoaded Inverted Pendulum (SLIP) has been widely exploited in both biomechanical and robotics research due to its simple form in mathematics and high accuracy in fitting experimental biology data. However the intrinsic nonlinearity of the SLIP dynamics makes accurate analytical representation unavailable. Traditional methods take advantage of numerical integration to handle this issue while several existing analytical approximations focusing on 2DSLIP model. The 3DSLIP suitable to physical reality is rarely investigated. This paper presents a novel perturbationbased approach to obtain the closedform analytical approximations of the 3DSLIP model in stance phase. In contrast to existing work ignoring the gravitational forces, the proposed approach just relies on assumptions of small leg compression and small leg swept angle. The performance of the derived approximations has been evaluated via comprehensive numerical analysis. The quality of accurate apex prediction promises the approximation as an advantageous and reliable tool for locomotion control of legged robots.

Walking Control of Biped Robots on Uneven Terrains Based on SLIP Model Having humanlike legged structure, biped robots are regarded as the most promising robots that can take the place of human to work in the environments designed for human beings. To this end, it is the premise for biped robots to achieve stable walking on uneven ground. This paper presents a control strategy for a biped robot based on springloaded inverted pendulum (SLIP) model, which controls the joint torque of the robot by obtaining the errors of length and angular position of virtual spring legs. Additionally, this paper proposes a new control method of adjusting the length of legs to enable the robot to achieve stable walking on unstructured terrains, such as staircases. In the end, the simulation results corroborate the effectiveness of the proposed approaches.