Gait Transitions for Quasi-static Hexapedal Locomotion on Level Ground

Abstract

As robot bodies become more capable, the motivation grows to better coordinate them-whether multiple limbs attached to a body or multiple bodies assigned to a task. This paper introduces a new formalism for coordination of periodic tasks, with specific application to gait transitions for legged platforms. Specifically, we make modest use of classical group theory to replace combinatorial search and optimization with a computationally simpler and conceptually more straightforward appeal to elementary algebra. We decompose the space of all periodic legged gaits into a cellular complex indexed using "Young Tableaux", making transparent the proximity to steady state orbits and the neighborhood structure. We encounter the simple task of transitioning between these gaits while locomoting over level ground. Toward that end, we arrange a family of dynamical reference generators over the "Gait Complex" and construct automated coordination controllers to force the legged system to converge to a specified cell's gait, while assessing the relative static stability of gaits by approximating their stability margin via transit through a "Stance Complex". To integrate these two different constructs-the Gait Complex describing possible gaits, the Stance Complex defining safe locomotion-we utilize our compositional lexicon to plan switching policies for a hybrid control approach. Results include automated gait transitions for a variety of useful gaits, shown via tests on a hexapedal robot. Abstract As robot bodies become more capable, the motivation grows to better coordinate them-whether multiple limbs attached to a body or multiple bodies as signed to a task. This paper introduces a new formalism for coordination of periodic tasks. with specific application to gaitlransitions for legged platforms. Specifically. we make modest use of classical group theory to replace combinatorial search and optimization with a computationally simpler and conceptually more straightforward appeal to elementary algebra.We decompose the space of all periodic legged gaits into a cellular complex in dexed using "Young Tableaux", making transparent the proximity to steady state orbits and the neighborhood structure. We encounter the simple task of transition ing between these gaits while locomoting over level ground. Toward that end. we arrange a family of dynamical reference generators over the "Gait Complex" and construct automated coordination controllers to force the legged system to converge to a specified cell's gait, while assessing the relative static stability of gaits by ap proximating their stability margin via transit through a "Stance Complex". To in tegrate these two different constructs-the Gait Complex describing possible gaits, the Stance Complex defining safe locomotion-we utilize our compositional lexicon to plan switching policies for a hybrid control approach. Results include automated gait transitions for a variety of useful gaits, shown via tests on a hexapedal robot.

Toward a vocabulary of legged leaping

“…In [29] a cell complex [30] was used to index all possible abstract coordination schemes that a legged machine might undertake and in [31] this cell complex was used to organize the possible gait transitions and recovery strategies of a quasistatic vertical climbing robot, treating the varying ground contact conditions experienced along the way as mere "noise" shown to be robustly rejected by a proper feedback implementation of the coordination controller.…”

Disturbance detection, identification, and recovery by gait transition in legged robots

“…Particularly with RHex-style machines such as EduBot, equipped with a single actuator per leg, the coordination of phase during active locomotion while avoiding a fall can be challenging. In planning and executing the gait recovery mechanism that we report here, we build upon prior work in topological gait classification, analysis, and control [30]. For this application, we signal a gait recovery transition for the scenario where the robot accidentally breaks a leg, resulting in an asymmetric five-legged gait for a hexapedal machine.…”

“…A total of 1082 unique gait orderings exist for a hexapedal robot [30], of which the alternating tripod is both uniquely fast and stable. Upon loss of a leg, however, we have a fivelegged system, for which only 150 unique timings exist, and the now "5-legged" tripod gait no longer maintains stability.…”

“…Our previous work in this problem domain associates Young Tabloids with gait cycles on a high dimensional torus -the phase space of multi-legged gaits -and uses a simple control policy to place global attractors at desired gait cycles [30]. While that prior work deals with the use of tabloids in correspondence with an algebra over which to plan gait transitions, we are now faced with the scenario of changing dimensionality, by which losing a leg forces us to consider gaits on a 5-dimensional torus rather than six.…”

“…Our gait classification formalism [30] adapts Young Tabloids [31], representations of the partitions of a set of unique integers, 1 . .…”