Human Balancing on a Log: A Switched Multi-Layer Controller

TL;DR

The paper addresses balancing a human on a fixed log, a task with highly unstable contact dynamics, by designing a switched, multi-layer controller that pairs an upper-layer LQR planner with lower-layer PID trackers. A three-case switching logic (Case 1, Case 2, Case 3) governs system behavior, with nonlinear transformations translating planned states into ankle angle references, and a muscle-activation extension to enhance biological plausibility. Simulations demonstrate robust stabilization under varied initial conditions and disturbances for both a torque-based controller and a muscle-activation model, highlighting the benefits of modular, interpretable control in unstable contact scenarios. The work advances bio-inspired control design for unstable, non-fixed-foot interactions and informs the development of more realistic, muscle-aware controllers for human-balancing tasks.

Abstract

We study the task of balancing a human on a log that is fixed in place. Balancing on a log is substantially more challenging than balancing on a flat surface due to increased instability -- nonetheless, we are able to balance by composing simple (e.g., PID, LQR) controllers in a bio-inspired switched multi-layer configuration. The controller consists of an upper-layer LQR planner (akin to the central nervous system) that coordinates ankle and hip torques, and lower-layer PID trackers (akin to local motor units) that follow this plan subject to nonlinear dynamics. The controller switches between three operational modes depending on the state of the human. The efficacy of the controller is verified in simulation, where our controller is able to stabilize the human for a variety of initial conditions and disturbances. We also introduce a controller that outputs muscle activations to perform the same balancing task.

Figures (7)

• Figure 1: (Left) Human balancing on a log. We use right-hand sign convention for angles; here, $\beta$ and $\theta$ have negative values. (Right) Schematic of muscle-based model, described in Section \ref{['sec:muscle_controller']}. Here, instead of applying torques to the ankle and hip joints, we manipulate joints using simplified muscles.
• Figure 2: For visual simplicity, we omit derivatives from the diagrams; wherever a state is used (e.g., $\theta$), assume that its derivative (e.g., $\dot{\theta}$) is also used. (Left) General control strategy. (Center) Control strategy for Case 1: ankle and hip controllers are decoupled. (Right) Control strategy for Cases 2 and 3: the upper-layer LQR controller produces hip torque and desired states ($\text{COM}^\text{des}_x$ for Case 2 and $x^\text{des}_\text{contact}$ for Case 3) for the ankle. We apply a nonlinear transformation ('NL') on the desired states to obtain the desired foot angle $\theta$; this is tracked by a lower-layer PID controller which outputs ankle torque.
• Figure 3: Switched controller: cases and transition rules.
• Figure 4: Geometric setup of simple muscle-based model.
• Figure 5: Control strategy for muscle-based actuation. 'NL' represents a nonlinear transformation that takes the desired contact point and gives a desired angle. PID and LQR outputs undergo a filter that ensures smoothness, positivity, and appropriate scaling of the final muscle activation $a_i$; the specific filter equations vary slightly between the two. For visual simplicity, we omit derivatives from the diagrams; wherever a state is used (e.g., $\theta$), assume that its derivative (e.g., $\dot{\theta}$) is also used.