This paper explores the benefits of using multiple gaits in a single robot. Inspired by nature, where humans and animals use different gaits to increase their energetic economy, we analyzed how increasing speed affects the choice of gait, and how the choice of gait influences optimal speed. To this end, we used optimal control as a tool to identify motions that minimize the cost of transport of two detailed models: a planar biped and a planar quadruped. Both of these models are actuated with high compliance series elastic actuators that enable a rich set of natural dynamics. These models have damping in their springs, feet with mass, and realistic limitations on actuator torques and velocities. They therefore serve as an intermediary between past simpler models and hardware. We discovered optimal motions with an established multiple shooting implementation that relies on pre-defined contact sequences, and with a direct collocation implementation in which the footfall pattern was an outcome of the optimization. Both algorithms confirmed findings from biology. For both models, changing gaits as speed varies leads to greatly increased energetic economy. For bipeds, the optimal gaits were walking at low speeds, grounded running at intermediate speeds, and running at high speeds. For quadrupeds, the optimal gaits were four-beat walking at low speeds and trotting at intermediate speeds. At high speeds, galloping and trotting were the best gaits, with nearly equal performance. We found that the transition between gaits was primarily driven by damping losses and negative actuator work, with collisions playing a relatively small role.

In this paper, we systematically investigate passive gaits that emerge from the natural mechanical dynamics of a bipedal system. We use an energetically conservative model of a simple spring-leg biped that exhibits well-defined swing leg dynamics. Through a targeted continuation of periodic motions of this model, we systematically identify different gaits that emerge from simple bouncing in place. We show that these gaits arise along one-dimensional manifolds that bifurcate into different branches with distinctly different motions. The branching is associated with repeated breaks in symmetry of the motion. Among others, the resulting passive dynamic gaits include walking, running, hopping, skipping and galloping. Our work establishes that the most common bipedal gaits can be obtained as different oscillatory motions (or nonlinear modes) of a single mechanical system with a single set of parameter values. For each of these gaits, the timing of swing leg motion and vertical motion is matched. This work thus supports the notion that different gaits are primarily a manifestation of the underlying natural mechanical dynamics of a legged system. Our results might explain the prevalence of certain gaits in nature, and may provide a blueprint for the design and control of energetically economical legged robots.

Despite enhancements in the development of robotic systems, the energy economy of today's robots lags far behind that of biological systems. This is in particular critical for untethered legged robot locomotion. To elucidate the current stage of energy efficiency in legged robotic systems, this paper provides an overview on recent advancements in development of such platforms. The covered different perspectives include actuation, leg structure, control and locomotion principles. We review various robotic actuators exploiting compliance in series and in parallel with the drive-train to permit energy recycling during locomotion. We discuss the importance of limb segmentation under efficiency aspects and with respect to design, dynamics analysis and control of legged robots. This paper also reviews a number of control approaches allowing for energy efficient locomotion of robots by exploiting the natural dynamics of the system, and by utilizing optimal control approaches targeting locomotion expenditure. To this end, a set of locomotion principles elaborating on models for energetics, dynamics, and of the systems is studied.

In this paper we use optimal control on a geared electric DC motor to compare the energetic efficiency of a simulation of conceptual monoped hoppers with either parallel elastic actuation (PEA) or series elastic actuation (SEA). The energy is measured using three cost functions: positive actuator work, electrical losses, and positive electrical work. For PEA, the presence of the motor inertia in the collision losses leads to increased collision losses at large transmission ratios, which lead to energetically costly compensatory strategies where the SEA is at its most efficient. At small transmission ratios, the motor force increases for both cases, leading to increased thermal losses. In agreement with those theoretical predictions, our work shows that for positive actuator work and positive electrical work the optimal parameter choice for SEA is significantly more energetically efficient than the optimal choice for PEA. For electrical losses, a suitable choice of the transmission ratio can lead to negligible cost values for both actuator concepts.

Inspired by the locomotive advantages that an articulated spine enables in quadrupedal animals, we explore and quantify the energetic effect that an articulated spine has in legged robots. We compare two model instances of a conceptual planar quadruped: one with a traditional rigid main body and one with an articulated main body with an actuated spinal joint. Both models feature four distinct legs, series elastic actuation, distributed mass in all body segments, and limits on actuator torque and speed. Using optimal control to find the energetically optimal joint trajectories, actuator inputs, and footfall timing, we examine and compare the positive mechanical work cost of transport of both models across multiple gaits and speeds. Our results show that an articulated spine increases the maximum possible speed and improves the locomotor economy at higher velocities, especially for asymmetrical gaits. The driving factors for these improvements are the same mechanistic effects that facilitate asymmetrical gaits in nature: improved leg recirculation, elastic energy storage in the spine, and enlarged stride lengths.