Control-theoretic approaches to gait termination in bipedal robots
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Date
2025-04
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University of New Brunswick
Abstract
Gait is a fundamental aspect of legged locomotion, playing a crucial role in enabling bipedal robots to navigate diverse and unpredictable environments. However, the ability to safely and efficiently terminate gait is equally important, as it ensures the robot's stability when transitioning from motion to a standstill.
This thesis addresses the problem of gait termination in ݊-link, underactuated point-feet bipeds that use dynamic notion of stability, known as limit cycle walkers. Using the whole-body dynamics of the robot, I present a unified gait termination solution applicable across all such walkers. This result is achieved by introducing a dynamical system model specifically for gait termination, integrated with existing walking models through a stable switching control strategy. To stabilize this model, I explore the use of smooth controllers. My analysis reveals that while such controllers may achieve local stabilization, the presence of nonholonomic contact point constraints limits the size of the region over which smooth stabilization is possible. By applying Sontag’s condition, I demonstrate that smooth control cannot ensure asymptotic stabilization over sufficiently large Regions of Attraction (ROA). However, Ishow that the system satisfies the Lie Algebra Rank Condition (LARC), indicating that it remains controllable. This controllability enables the design of a nonsmooth switching control strategy that, unlike computationally demanding optimization-based methods such as Model Predictive Control (MPC), primarily uses computationally efficient switching controllers and resorts to more intensive methods only when necessary to maintain constraints.
The proposed switching controller comprises two sub-controllers: a balancing controller and a Ground Reaction Force (GRF) controller. The GRF controller consists of two components: one based on Nagumo’s theorem for analytically enforcing constraints, and a numerical component for handling complex cases where analytical methods are inadequate. To improve the efficiency of this numerical component, I introduce a novel Differential Dynamic Programming (DDP) approach, tailored to handle inequality constraints involving both state and control variables. I analytically prove the stability of the proposed switching strategy. Simulations confirm that this approach effectively manages contact constraints for most of the trajectory, utilizing computationally intensive controllers only when required, thereby enhancing real-time performance of the control framework.