Extending the lossy Spring-Loaded Inverted Pendulum model with a slider-crank mechanism

Abstract

Spring Loaded Inverted Pendulum (SLIP) model has a long history in describing running behavior in animals and humans as well as has been used as a design basis for robots capable of dynamic locomotion. Anchoring the SLIP for lossy physical systems resulted in newer models which are extended versions of original SLIP with viscous damping in the leg. However, such lossy models require an additional mechanism for pumping energy to the system to control the locomotion and to reach a limit-cycle. Some studies solved this problem by adding an actively controllable torque actuation at the hip joint and this actuation has been successively used in many robotic platforms, such as the popular RHex robot. However, hip torque actuation produces forces on the COM dominantly at forward direction with respect to ground, making height control challenging especially at slow speeds. The situation becomes more severe when the horizontal speed of the robot reaches zero, i.e. steady hoping without moving in horizontal direction, and the system reaches to singularity in which vertical degrees of freedom is completely lost. To this end, we propose an extension of the lossy SLIP model with a slider-crank mechanism, SLIP-SCM, that can generate a stable limit-cycle when the body is constrained to vertical direction. We propose an approximate analytical solution to the nonlinear system dynamics of SLIP-SCM model to characterize its behavior during the locomotion. Finally, we perform a fixed-point stability analysis on SLIP-SCM model using our approximate analytical solution and show that proposed model exhibits stable behavior in our range of interest.

New Variable Passive-Compliant Element Design for Quadruped Adaptation to Stiffness-Varying Terrain

“…The lift-off time is set to be equal to the time of the maximum compression, which is uniquely defined for the lossy SLIP model according to the equation (14). The work presented in [33] follows a similar idea by utilizing a Newton-Raphson method to find an approximate solution tlo' of (17), while supplying an initial estimate with tlo≈2tb. The method is iterative in nature but the authors use the first iteration as an approximation of the result:…”

“…The work presented in [33] follows a similar idea by utilizing a Newton-Raphson method to find an approximate solution t lo ' of (17), while supplying an initial estimate with t lo ≈ 2t b . The method is iterative in nature but the authors use the first iteration as an approximation of the result:…”

Trotting Motion of the Quadruped Model with Two Spinal Joints and Its Dynamics Features

“…A general finding reveals that when the humans or mammals run, the legs act as springs and experience a compression and extension process to improve the energy efficiency and the compliance of the interaction with the ground [2]. Accordingly, a general model template, Spring Loaded Inverted Pendulum (SLIP), was proposed [3] and extended [4][5][6][7]. To analyze the intuitive motion mechanism of quadruped motion at different gaits, the planar model including a rigid body and four massless springy legs was established based on the SLIP model [8].…”