Understanding and Improving Locomotion: The Simultaneous Optimization of Motion and Morphology in Legged Robots

There exist many open design questions in the field of legged robotics. Should leg extension and retraction occur with a knee or a prismatic joint? Will adding a compliant ankle lead to improved energetics compared to a point foot? Should quadrupeds have a flexible or a rigid spine? Should elastic elements in the actuation be placed in parallel or in series with the motors? Though these questions may seem basic, they are fundamentally difficult to approach. A robot with either discrete choice will likely need very different components and use very different motion to perform at its best. To make a fair comparison between two design variations, roboticists need to ask, is the best version of a robot with a discrete morphological variation better than the best version of a robot with the other variation? In this dissertation, I propose to answer these type of questions using an optimization based approach. Using numerical algorithms, I let a computer determine the best possible motion and best set of parameters for each design variation in order to be able to compare the best instance of each variation against each other. I developed and implemented that methodology to explore three primary robotic design questions. In the first, I asked if parallel or series elastic actuation is the more energetically economical choice for a legged robot. Looking at a variety of force and energy based cost functions, I mapped the optimal motion cost landscape as a function of configurable parameters in the hoppers. In the best case, the series configuration was more economical for an energy based cost function, and the parallel configuration was better for a force based cost function. I then took this work a step further and included the configurable parameters directly within the optimization on a model with gear friction. I found, for the most realistic cost function, the electrical work, that series was the better choice when the majority of the transmission was handled by a low-friction rotary-to-linear transmission. In the second design question, I extended this analysis to a two-dimensional monoped moving at a forward velocity with either parallel or series elastic actuation at the hip and leg. In general it was best to have a parallel elastic actuator at the hip, and a series elastic actuator at the leg. In the third design question, I asked if there is an energetic benefit to having an articulated spinal joint instead of a rigid spinal joint in a quadrupedal legged robot. I found that the answer was gait dependent. For symmetrical gaits, such as walking and trotting, the rigid and articulated spine models have similar energetic economy. For asymmetrical gaits, such as bounding and galloping, the articulated spine led to significant energy savings at high speeds. The combination of the above studies readily presents a methodology for simultaneously optimizing for motion and morphology in legged robots. Aside from giving insight into these specific design questions, the technique can also be extended to a variety of other design questions. The explorations in turn inform future hardware development by roboticists and help explain why animals in nature move in the ways that they do.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144074/1/yevyes_1.pd

An Overview on Principles for Energy Efficient Robot Locomotion

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

An extension to the collisional model of the energetic cost of support qualitatively explains trotting and the trot–canter transition

The majority of terrestrial mammals adopt distinct, discrete gaits across their speed range. Though there is evidence that walk, trot and gallop may be selected at speeds consistent with minimizing metabolic cost (Hoyt and Taylor, 1981, Nature, 291, 239–240), the mechanical causes underlying these costs and their changes with speed are not well understood. In particular, the paired, near‐simultaneous contacts of the trot is puzzling as it appears to demand a high mechanical work that could easily be avoided with distributed contacts, as with a “running walk” gait or “tolt.” Here, a simple condition is derived—a ratio including the pitch moment of inertia and back length—for which trotting is energetically advantageous because it avoids the energetic consequences of pitching. Pitching could also be avoided if the impulses from the legs were orientated through the center of mass. A range of idealized gaits is considered that achieve this zero‐pitch condition, and work minimization predicts a transition from trot to canter at intermediate speeds. This can be understood from the geometric principles of achieving a “pseudoelastic” collision with each impulse (Ruina et al., 2005, J Theoretical Biol, 14, 170‐192). However, at high speeds, a transition back to trot is predicted that is not observed in nature

An Overview on Principles for Energy Efficient Robot Locomotion.

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