Velocity Decomposition-Enhanced Control for Point and Curved-Foot Planar Bipeds Experiencing Velocity Disturbances

Abstract

This paper extends the use of velocity decomposition of underactuated mechanical systems to the design of an enhanced hybrid zero dynamics (HZD)-based controller for biped robots. To reject velocity disturbances in the unactuated degree-of-freedom, a velocity decomposition-enhanced controller implements torso and leg offsets that are proportional to the error in the time derivative of the unactuated velocity. The offsets are layered on top of an HZD-based controller to preserve simplicity of implementation. Simulation results with a point-foot, three-link planar biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. Curved feet are implemented in simulation and show that the proposed control method is valid for both point-foot and curved-foot planar bipeds. Performance of each controller is assessed by (1) the magnitude of the disturbance it can reject by numerically computing the basin of attraction, (2) the speed of return to nominal step velocity following a disturbance at every point of the gait cycle, and (3) the energetic efficiency, which is measured via the specific cost of transport. Several gaits are analyzed to demonstrate that the observed trends are consistent across different walking speeds.

Quantifying the effect of sagittal plane joint angle variability on bipedal fall risk

“…Thus, the nominal motion was defined as: where α k were the polynomial coefficients chosen to minimize a weighted torque-square objective function [ 10 ]. Because previous research indicated that speed has an impact on falls [ 15 , 21 , 22 , 46 ], three different nominal gaits from [ 10 ] were tested—slow (0.98 m/s), medium (1.30 m/s), and fast (1.56 m/s). The models associated with each gait were adult-sized, although each had somewhat different mass and length parameters because each gait was associated with a different person or group.…”

“…One challenge with predicting falls is that they have many potential causes. Robotic studies have primarily evaluated falls due external factors, such as walking across uneven terrain [ 13 ] or due to velocity disturbances such as a push [ 14 , 15 ]. These works also tend to focus on discrete, rather than continuous, perturbations.…”

Terrain-blind walking of planar underactuated bipeds via velocity decomposition-enhanced control

“…The velocity decomposition-enhanced controller was also implemented on a three-link biped model with curved feet, which considerably reduced the energetic cost of walking relative to the point-foot case (Fevre et al, 2019). The velocity disturbance rejection performance of the velocity decomposition-enhanced controller on the curved-foot model was consistent with the point-foot model, and switching from one model to the other did not require re-tuning the controller gains.…”

“…The velocity disturbance rejection performance of the velocity decomposition-enhanced controller on the curved-foot model was consistent with the point-foot model, and switching from one model to the other did not require re-tuning the controller gains. Moreover, the complexity of the proposed control strategy remains the same with the addition of curved feet (Fevre et al, 2019), which is another desirable aspect of low-level feedback controllers for extension to more complex biped robots.…”

“…Velocity disturbances. Velocity disturbances were analyzed in Fevre et al (2018Fevre et al ( , 2019 with the results briefly summarized in the following. In the deceleration case, velocity decomposition-enhanced control and transverse linearization feedback control returned the robot to within 2% of the steady-state step velocity in 2.6 and 2.4 steps on average, respectively, while the HZD-based controller did so in 5.3 steps.…”