Underactuated Bipedal Walking Research Articles

Stochastic stability analysis of legged locomotion using unscented transformation

In this manuscript, we present a novel method for estimating the stochastic stability characteristics of metastable legged systems using the unscented transformation. Prior methods for stability analysis in such systems often required high-dimensional state space discretization and a broad set of initial conditions, resulting in significant computational complexity. Our approach aims to alleviate this issue by reducing the dimensionality of the system and utilizing the unscented transformation to estimate the output distribution. This technique allows us to account for multiple sources of uncertainty and high-dimensional system dynamics, while leveraging prior knowledge of noise statistics to inform the selection of initial conditions for experiments. As a result, our method enables the efficient assessment of controller performance and analysis of parametric dependencies with fewer experiments. To demonstrate the efficacy of our proposed method, we apply it to the analysis of a one-dimensional hopper and an underactuated bipedal walking simulation with a hybrid zero dynamics controller.

Velocity-Based Gait Planning for Underactuated Bipedal Robot on Uneven and Compliant Terrain

This article develops a gait planning method for underactuated bipedal robot on uneven and compliant terrain. First, we employ a linear spring-damper model to describe foot-ground compliant contact, and establish a decoupled robot–ground three-dimensional dynamic mode. Second, based on a velocity-based bipedal stability definition and human walking characteristics, we propose a gait planning method to realize underactuated bipedal walking on uneven and compliant terrain. We decouple bipedal gait planning into sagittal and lateral master-slave ones. By planning the motion state of Center-of-Mass (CoM) of a robot, we make the movement of lateral and sagittal coincident such that bipedal walking is realized. Finally, underactuated bipedal walking with an average walking speed of 0.216 m/s and a step length of 183.9 mm is realized on uneven terrain where the maximum height of unevenness is 32 mm. The experimental results show that underactuated bipedal walking can be realized on uneven and compliant terrain by using the proposed method to control robot CoM and track its desired velocity.

3-D Underactuated Bipedal Walking via H-LIP Based Gait Synthesis and Stepping Stabilization

In this article, we holistically present a hybrid-linear inverted pendulum (H-LIP) based approach for synthesizing and stabilizing 3-D foot-underactuated bipedal walking, with an emphasis on thorough hardware realization. The H-LIP is proposed to capture the essential components of the underactuated and actuated part of the robotic walking. The robot walking gait is then <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">directly</i> synthesized based on the H-LIP. We comprehensively characterize the periodic orbits of the H-LIP and provably derive the stepping stabilization via its step-to-step (S2S) dynamics, which is then utilized to approximate the S2S dynamics of the horizontal state of the center of mass of the robotic walking. The approximation facilities a H-LIP based stepping controller to provide desired step sizes to stabilize the robotic walking. By realizing the desired step sizes, the robot achieves dynamic and stable walking. The approach is fully evaluated in both simulation and experiment on the 3-D underactuated bipedal robot Cassie, which demonstrates dynamic walking behaviors with both high versatility and robustness.

Feedforward control for underactuated bipedal walking on compliant continuous steps with varying height

This study develops a feedforward control strategy based on the motion state of center-of-mass (CoM) of a robot for underactuated biped robot stable walking on compliant continuous steps with a known varying height. First, considering ground deformation, a compliant contact model is employed to characterize foot-ground interaction, and a robot–step coupling dynamic model of sagittal and lateral planes are established through decoupling modelling. Second, based on the gait characteristics of human variable-step walking, a feedforward control strategy based on the motion state of CoM is proposed. Varying height step is equivalent to varying slope, an equivalent slope angle and a desired step length can be calculated for each step according to their height. Underactuated bipedal walking control is decoupled into sagittal and lateral master-slave control. The velocity of robot CoM is considered as a system output. It is controlled through the displacement of CoM in a single walking cycle, and thus walking is stabilized. By the proposed method, the walking system is modelled as a polynomial with definite number of degrees and the controlled input is derived through a simple inverse operation on it. Its effectiveness is validated through simulations in an environment with a step varying height of less than 0.032 m. Simulation results show that the proposed method can improve the tracking performance of robot CoM velocity on varying height steps, as compared to a hybrid zero dynamic (HZD)-based controller.

A Stabilization Method Based on an Adaptive Feedforward Controller for the Underactuated Bipedal Walking with Variable Step-Length on Compliant Discontinuous Ground

Both compliance and discontinuity are the common characteristics of the real ground surface. This paper proposes a stabilization method for the underactuated bipedal locomotion on the discontinuous compliant ground. Unlike a totally new control method, the method is actually a high-level control strategy developed based on an existing low-level controller meant for the continuous compliant ground. As a result, although the ground environment is more complex, the calculation cost for the robot walking control system is not increased. With the high-level control strategy, the robot is able to adjust its step-length and velocity simultaneously to stride over the discontinuous areas on the compliant ground surface. The effectiveness of the developed method is validated with a numerical simulation and a physical experiment.

A Position-Domain Adaptive Control Method for Underactuated Bipedal Walking on a Compliant Ground

Motivated by the potential use of humanoid-robot in real environment, a position-domain adaptive control strategy is developed to stabilize the underactuated bipedal walking on a compliant ground. First, the robot-ground system is modeled as a rigid kinematical chain coupled with a spring-damper system. Then by observing the simulation result of walking on compliant ground, we find the improvement of walking stability can be realized by controlling the initial velocity of robot’s center-of-mass (COM) of each walking cycle. In consideration of the highly-complicated impact of real road surface on direct velocity control, through the analysis on the relationship between the robot’s COM velocity and its foot vertical velocity, the robot’s state is parameterized by the normalized relative vertical position between both the feet, and the control of robot’s COM initial velocity of current cycle is realized by controlling the relative vertical velocity between the robot’s two feet during the previous impact phase. To realize it, an adaptive feedback linearization control strategy is developed in position-domain. Finally, the availability and adaptability of this method are validated through simulations: Specific to three initial gaits, on four compliant ground with different damping parameters, the underactuated bipedal walking is stabilized and the performance is improved.

Efficiency analysis of telescopic-legged bipedal robots

This paper investigates the stability of underactuated bipedal walking incorporating telescopic-leg actuation. In human walking, knee joints of swing and support legs are bent and stretched. The telescopic legs mimic the motion of the center of mass of human legs via their telescopic motion during the stance phase. First, underactuated telescopic-legged biped robot models are introduced. Second, an output-following control law is applied to the linearized equation of motion of the robot, and the controlled robot’s equation is then specified as a linear time-varying system. The error transition equation is developed to evaluate the stability during the stance phase. Numerical calculations are performed to show the influences of leg telescopic motion on the stability.

Feedforward control for underactuated bipedal walking on varying compliant slopes

In this paper, a feedforward control strategy is proposed to enable stable underactuated bipedal walking on varying compliant slopes with a known inclination angle, to handle the variation in natural environments. First, spring–damper units were employed in the horizontal and vertical directions to model the compliant ground, which is described as a rigid kinematic chain coupled with a spring–damper system. Second, a new definition of stable underactuated bipedal walking, based on walking speed, was proposed. Stable walking is achieved by adjusting the velocity of the biped’s center of mass (CoM) within limits that have been proven to allow at least one walking cycle. The proposed feedforward control strategy was based on the motion state of a robot’s CoM, using the new definition of stability and inspired by the gait characteristics of human walking on varying slopes. Speed control is realized by adjusting the displacement of the CoM with the change of slope to achieve stable walking. Finally, simulations were conducted to validate the proposed controller. The simulation results demonstrate that stable walking is achieved on varying compliant slopes by implementing the proposed control strategy.