Arbitrary Symmetric Running Gait Generation for an Underactuated Biped Model

Abstract

This paper investigates generating symmetric trajectories for an underactuated biped during the stance phase of running. We use a point mass biped (PMB) model for gait analysis that consists of a prismatic force actuator on a massless leg. The significance of this model is its ability to generate more general and versatile running gaits than the spring-loaded inverted pendulum (SLIP) model, making it more suitable as a template for real robots. The algorithm plans the necessary leg actuator force to cause the robot center of mass to undergo arbitrary trajectories in stance with any arbitrary attack angle and velocity angle. The necessary actuator forces follow from the inverse kinematics and dynamics. Then these calculated forces become the control input to the dynamic model. We compare various center-of-mass trajectories, including a circular arc and polynomials of the degrees 2, 4 and 6. The cost of transport and maximum leg force are calculated for various attack angles and velocity angles. The results show that choosing the velocity angle as small as possible is beneficial, but the angle of attack has an optimum value. We also find a new result: there exist biped running gaits with double-hump ground reaction force profiles which result in less maximum leg force than single-hump profiles.

SLIP-Based Control of Bipedal Walking Based on Two-Level Control Strategy

“…For future work, this control strategy can guide the real robot walking and running, allowing determination of robustness to terrain softness. Also, SLIP could be replaced by an active template model, like point mass biped (PMB), 26 which should be able to generate more general gaits including asymmetric trajectories.…”

A survey on underactuated robotic systems: Bio-inspiration, trajectory planning and control

“…ATRIAS [29] is an underactuated bio-inspired biped robots that attracts much attentions during the past decade. SLIP (spring loaded inverted pendulum) [123,124] and PMB (point mass biped) [125] are basic underactuated models to generate and control biped running gaits with natural properties, where PMB has been shown to be capable of generating more general gaits than SLIP.…”

A Case Study on Influence of Utilizing Hill-Type Muscles on Mechanical Efficiency of Biped Running Gait

“…The leg force is denoted by r F and the leg angle, with respect to vertical, by θ. The degree-4 polynomial path is similar qualitatively to the SLIP trajectory and can generate running gaits with any desired initial condition of the stance phase with the correct initial and final accelerations [9]. The PMB path in the stance phase is considered as ,…”

“…in which coefficients i a are calculated using the COM initial position, velocity, and acceleration. Combining the path equation with the dynamic equation of the PMB system leads to a second order nonlinear differential equation [9]. By solving this equation numerically, the trajectory is calculated as a function of time.…”

“…Also, the Point Mass Biped (PMB) model consisting of a point mass and prismatic force actuator can generate biped walking and running gaits by minimizing mechanical work costs [7], as well as smoother force profiles by minimizing a hybrid cost function including mechanical work, leg force, and its derivatives [8]. PMB model has proven to be a more general model than a SLIP model, capable of generating arbitrary trajectories for bipedal running with singlehump and double-hump ground reaction force (GRF) profiles [9]. Minimal robots have been fabricated based on these models.…”