Algorithmic Foundations of Realizing Multi-Contact Locomotion on the Humanoid Robot DURUS

Abstract

This paper presents the meta-algorithmic approach used to realize multi-contact walking on the humanoid robot, DURUS. This systematic methodology begins by decomposing human walking into a sequence of distinct events (e.g. heel-strike, toe-strike, and toe push-off). These events are converted into an alternating sequence of domains and guards, resulting in a hybrid system model of the locomotion. Through the use of a direct collocation based optimization framework, a walking gait is generated for the hybrid system model emulating human-like multi-contact walking behaviors -additional constraints are iteratively added and shaped from experimental evaluation to reflect the machine's practical limitations. The synthesized gait is analyzed directly on hardware wherein feedback regulators are introduced which stabilize the walking gait, e.g., modulating foot placement. The end result is an energyoptimized walking gait that is physically implementable on hardware. The novelty of this work lies in the creation of a systematic approach for developing dynamic walking gaits on 3D humanoid robots: from formulating the hybrid system model to gait optimization to experimental validation refined to produce multi-contact 3D walking in experiment.

Dynamic Output Controllers for Exponential Stabilization of Periodic Orbits for Multidomain Hybrid Models of Robotic Locomotion

“…HZD-based controllers have been validated numerically and experimentally for (i) 2D and 3D bipedal robots, including RABBIT [17,18], MA-BEL [19][20][21], ERNIE [22], AMBER [23], ATRIAS [24][25][26][27], and DURUS [28,29] prototypes, (ii) powered prosthetic legs [30][31][32][33], (iii) exoskeletons [34], (iv) monopedal robots [35,36], and (v) quadruped robots [37]. In the HZD approach, a set of output functions, referred to as virtual constraints, is defined for the continuous-time dynamics of the system and asymptotically driven to zero by partial linearizing feedback controllers [38].…”

Virtual Model Control for Quadruped Robots

“…Boston Dynamics employed the idea of spring loaded inverted pendulum (SLIP) model to guide the locomotion of Bigdog [9]. Researchers in University of Michigan proposed a hybrid zero dynamics (HZD) method for planar biped walkers [10] and it was employed to prove the local stability of PD controlled bipedal walking robots [11], [12]. Similarly, a method of virtual constraints (VC) was combined with model predictive control (MPC) and quadratic programming (QP) to develop a hierarchical nonlinear control algorithm for stable quadrupedal locomotion patterns [13].…”

Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion

“…For mechanical systems with more than one degree of underactuation, the stability of walking gaits depends on the choice of the virtual constraints [30], [31]. Anthropomorphic heel-to-toe walking has been achieved in planar models [32,Chapter 10] and most recently in a 3D robot [18] using the HZD controllers. In particular, [18] presented an efficient optimization framework (motion planning) to generate HZD gaits.…”

“…Anthropomorphic heel-to-toe walking has been achieved in planar models [32,Chapter 10] and most recently in a 3D robot [18] using the HZD controllers. In particular, [18] presented an efficient optimization framework (motion planning) to generate HZD gaits. Although the gaits of [18] are stable, there is currently no systematic algorithm to choose asymptotically stabilizing virtual constraints for a given 3D walking gait.…”

“…In particular, [18] presented an efficient optimization framework (motion planning) to generate HZD gaits. Although the gaits of [18] are stable, there is currently no systematic algorithm to choose asymptotically stabilizing virtual constraints for a given 3D walking gait. We are trying to answer this fundamental question: how to present an effective optimization algorithm to choose stabilizing virtual constraints for a generated 3D gait with high degrees of underactuation?…”