Foot Placement Control for Bipedal Walking on Uneven Terrain: An Online Linear Regression Analysis Approach

Abstract

This paper presents a novel foot placement control algorithm for adaptive bipedal walking. In this method, the torso attitude and height are stabilized by synergic patterns so that the forward velocity and its change have a stable and nearly linear relation with the foot placement. Hence, our proposed online linear regression analysis well represents the local linear models by estimating continuously from measured data. Based on this estimation, an appropriate foot placement can be determined to control the forward velocity. Our simulation study successfully demonstrates the natural gait with accurate tracking of walking velocity, and the robustness of walking over uneven terrain.

Robust foot placement control for dynamic walking using online parameter estimation

“…where β 1 and β 2 replace the model-based coefficients, and β 3 accounts for the error terms expressed in (6) and (10).…”

“…Nakanishi et al [9] developed a framework to learn bipedal locomotion through movement primitives by locally weighted regression while the frequency of the learned trajectories is adjusted automatically by a frequency adaptation algorithm. You et al [10] used linear regression based on past measurements for updating the coefficients of an improved formulation based on Raibert's model to track a desired forward velocity more accurately. This method improved the system's flexibility to unknown changes, such as a mass offset, and was later extended to bipedal walking and running [11].…”

A study of nonlinear forward models for dynamic walking

“…Foot placement primarily determines the discrete nature of step-to-step transition, and thus the stability of walking and control of the robot movement [9], [21], [22]. As [22] said, the foot placement has an almost linear relationship between the velocity of robot.…”

“…Foot placement primarily determines the discrete nature of step-to-step transition, and thus the stability of walking and control of the robot movement [9], [21], [22]. As [22] said, the foot placement has an almost linear relationship between the velocity of robot. Hence given the robot state predicted by the forward simulation at the end of the current step, it should be very easy to use the gradient descent method to find an appropriate foot placement for the next step to reach a desired state.…”

Straight leg walking strategy for torque-controlled humanoid robots

“…Particularly, the humanoid WABIAN [11] could perform knee stretching walking by predefining the trajectory of supportleg's knee joint, and it could also realize heel-contact and toe-off motions with specially designed passive toe joints. Inspired by Raibert's work [12], [13] realized humanoid-like walking by determining foot placement via on-line linear regression, however it is hard to fully utilize ankle torque to help stabilizing.…”