Dynamic Walking: Toward Agile and Efficient Bipedal Robots

Abstract

Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review outlines the end-to-end process of methods that have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced-order models that capture essential walking behaviors to hybrid dynamical systems that encode the full-order continuous dynamics along with discrete foot-strike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiations on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is both agile and efficient. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 4 is May 3, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Invariance and Contraction in Geometrically Periodic Systems with Differential Inclusions

“…The nonlinear input-affine system used in dynamic walking studies [13][14][15]59], associated with the discrete instantaneous impact, can be formulated as a hybrid dynamics system:…”

Natural Multicontact Walking for Robotic Assistive Devices via Musculoskeletal Models and Hybrid Zero Dynamics

“…Even though bipedal locomotion is seemingly effortless for humans, achieving stable walking on robotic platforms is challenging as it requires accounting for discrete impact events, underactuation, and complicated nonlinear dynamics. Existing methods that have successfully demonstrated stable robotic locomotion include reduced-order models [2]- [5], model-based gait generation [6]- [8], and reinforcement learning [9]- [13]. Of these approaches, we are particularly interested in the Hybrid Zero Dynamics (HZD) method [14], [15], which is a mathematical approach leveraging the hybrid system model of locomotion, and capable of synthesizing provably stable [16] dynamic walking gaits on bipedal robots, encoded by impactinvariant periodic orbits.…”

“…Of these approaches, we are particularly interested in the Hybrid Zero Dynamics (HZD) method [14], [15], which is a mathematical approach leveraging the hybrid system model of locomotion, and capable of synthesizing provably stable [16] dynamic walking gaits on bipedal robots, encoded by impactinvariant periodic orbits. This method has been demonstrated on a number of robotic platforms and behaviors, including dynamic multicontact walking on 3D robots [8].…”

Inverse Dynamics Control of Compliant Hybrid Zero Dynamic Walking

“…However, implementing model-based planning and control methods on physical systems is typically non-trivial due to the inherent model inaccuracy, dynamically changing contact constraints, and possibly conflicting objectives for the robot which naturally arise in locomotion. It is due to these challenges that bipedal robots which exhibit simultaneously robust, efficient, and agile motions are rare in practice [21].…”