For a class of biped robots with impulsive dynamics and a non-empty set of passive gaits (unactuated, periodic motions of the biped model), we present a method for computing continuous families of locally optimal gaits with respect to a class of commonly used energetic cost functions (e.g., the integral of torque-squared). We compute these families using only the passive gaits of the biped, which are globally optimal gaits with respect to these cost functions. Our approach fills in an important gap in the literature when computing a library of locally optimal gaits, which often do not make use of these globally optimal solutions as seed values. We demonstrate our approach on a well-studied two-link biped model.

We present a homotopic approach to generating energetically optimal gaits for legged robots that maps passive (i.e., unactuated) gaits of an energetically conservative model of the robot to a model with user-defined target dynamics with dissipation and actuation (i.e., the more “realistic” legged model). Our core contribution is advancing the state-of-the-art towards a turn-key approach where the seed values are known by design and do not rely on domain-specific knowledge to generate or randomly guess across a range of energetic cost functions and desired gait properties (e.g., walking speed, hopping height, etc.), which can limit the usefulness of the typical optimization-based approach. We demonstrate this methodology on a parallel elastic actuated planar monoped with five degrees of freedom. Our work also demonstrates an explicit connection between passive gaits and optimally actuated motions, which has long been an area of interest in the fields of robotics and biome-chanics.

This article describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2-D and 3-D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g., closed-loop linkages), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly defined manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium configurations of the biped often belong to such manifolds, we use equilibria as “templates” from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2-D and 3-D biped walkers.

We present a strategy for generating period-one, open-loop walking gaits for multi-degree-of-freedom, planar biped walkers. Our approach uses equilibria of the dynamics as templates, which we connect to a family of period-one walking motions using numerical continuation methods. We define a gait as a fixed point of the walker's hybrid dynamics which resides in a state-time-control space consisting of the robot's post-impact state, switching time (the time at which the swing leg impacts the ground), and a finite set of design or control parameters. We demonstrate our approach on several physically-symmetric biped walkers. In particular, we prove that our approach reduces the search space for an initial gait in the state-time-control space to a one-dimensional search in switching time. We show that we can generates periodic motion without resorting to splines or reference trajectories. Finally, we compare our method to generating gaits with virtual holonomic constraints.

This paper presents a hybrid mechanical model for the Gibbot, a robot that dynamically locomotes along a vertical wall in a manner analogous to gibbons swinging between branches in the forest canopy. We focus on one particular gait, continuous-contact brachiation, which always has one handhold in contact with the wall. We use zero-cost, unstable solutions corresponding to horizontal brachiation, originally found by Gomes and Ruina, as templates to generate open-loop stable gaits in arbitrary directions. The first case considered is passive brachiation down a shallow slope, roughly corresponding to upside-down locomotion of the well-studied compass-gait biped. We then consider underactuated brachiation with a constant forcing term at the elbow to produce open-loop stable descending and ascending gaits.