A compliant ankle-actuated compass walker with triggering timing control

TL;DR

The paper addresses the limitations of passive compass gait locomotion by introducing triggering-controlled ankle actuation with compliant pushoff, implemented via series elastic actuators (SEAs). By formulating the TC-AACG model and conducting a comprehensive Poincaré stability analysis, it shows that pre-collision ankle pushoff—tuned through precompression ${r_0}$ and triggering angle ${\theta_s^{trig}}$—yields higher walking speeds at lower mechanical cost of transport (mCoT) than impulsive schemes, while maintaining robustness across a meaningful basin of attraction. The work provides extensive simulation-based insights into speed, energy efficiency, and stability trade-offs, demonstrating that judicious timing and stiffness enable efficient, robust locomotion on level and rough terrain. These findings offer practical design guidelines for SEA-based underactuated bipeds and advance the use of compliant ankle actuation for real-world robotic walking.

Abstract

Passive dynamic walkers are widely adopted as a mathematical model to represent biped walking. The stable locomotion of these models is limited to tilted surfaces, requiring gravitational energy. Various techniques, such as actuation through the ankle and hip joints, have been proposed to extend the applicability of these models to level ground and rough terrain with improved locomotion efficiency. However, most of these techniques rely on impulsive energy injection schemes and torsional springs, which are quite challenging to implement in a physical platform. Here, a new model is proposed, named triggering controlled ankle actuated compass gait (TC-AACG), which allows non-instantaneous compliant ankle pushoff. The proposed technique can be implemented in physical platforms via series elastic actuators (SEAs). Our systematic examination shows that the proposed approach extends the locomotion capabilities of a biped model compared to impulsive ankle pushoff approach. We provide extensive simulation analysis investigating the locomotion speed, mechanical cost of transport, and basin of attraction of the proposed model.

Figures (6)

• Figure 1: (a) The triggering controlled ankle actuated compass gait (TC-AACG) model with associated system parameters. (b) Configuration of the TC-AACG model at collision with associated velocity vectors.
• Figure 2: Locomotion phases and the transition events of the TC-AACG model. Transition from single support phase to single support pushoff or double support phase has a state-dependent nature.
• Figure 3: Fixed points of the TC-AACG model for $k=100\;N/m$ as a function of spring precompression and triggering angle along with their periodicity. $R1$, $R2$, and $R3$ represent the regions for which the spring is not triggered, spring is triggered, spring is triggered and extended in the single support phase, respectively. The subfigures illustrate the propulsive and impeding forces acting on the spring for four fixed points marked on the main figure.
• Figure 4: Horizontal speed (a) and mechanical cost of transport (b) of fixed points of the TC-AACG model as a function of spring precompression and triggering angle. The purple boundary in a) correspond to the region, ${\mathbf p}_{ssp}$, where the locomotion speed due to pre-collision pushoff is substantial. $p1$, $p2$, and $p3$ show the horizontal speed and mCoT for three fixed points.
• Figure 5: Area of basin of attraction of fixed points of the TC-AACG model as a function of spring precompression and triggering angle. For each subplot, $p1$, $p2$, $p3$, and $p^*$ show the area of BoA for the sample fixed points.