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

Dexterity, workspace and performance analysis of the conceptual design of a novel three-legged, redundant, lightweight, compliant, serial-parallel robot

In this article, the mechanical design and analysis of a novel three-legged, agile robot with passively compliant 4-degrees-of-freedom legs, comprising a hybrid topology of serial, planar and spherical parallel structures, is presented. The design aims to combine the established principle of the Spring Loaded Inverted Pendulum model for energy efficient locomotion with the accuracy and strength of parallel mechanisms for manipulation tasks. The study involves several kinematics and Jacobian based analyses that specifically evaluate the application of a non-overconstrained spherical parallel manipulator as a robot hip joint, decoupling impact forces and actuation torques, suitable for the requirements of legged locomotion. The dexterity is investigated with respect to joint limits and workspace boundary contours, showing that the mechanism stays well conditioned and allows for a sufficient range of motion. Based on the functional redundancy of the constrained serial-parallel architecture it is furthermore revealed that the robot allows for the exploitation of optimal leg postures, resulting in the possible optimization of actuator load distribution and accuracy improvements. Consequently, the workspace of the robot torso as additional end-effector is investigated for the possible application of object manipulation tasks. Results reveal the existence of a sufficient volume applicable for spatial motion of the torso in the statically stable tripodal posture. In addition, a critical load estimation is derived, which yields a posture dependent performance index that evaluates the risks of overload situations for the individual actuators

Mechanical design and analysis of a novel three-legged, compact, lightweight, omnidirectional, serial–parallel robot with compliant agile legs

In this work, the concept and mechanical design of a novel compact, lightweight, omnidirectional three-legged robot, featuring a hybrid serial–parallel topology including leg compliance is proposed. The proposal focusses deeply on the design aspects of the mechanical realisation of the robot based on its 3D-CAD assembly, while also discussing the results of multi-body simulations, exploring the characteristic properties of the mechanical system, regarding the locomotion feasibility of the robot model. Finally, a real-world prototype depicting a single robot leg is presented, which was built by highly leaning into a composite design, combining complex 3D-printed parts with stiff aluminium and polycarbonate parts, allowing for a mechanically dense and slim construction. Eventually, experiments on the prototype leg are demonstrated, showing the mechanical model operating in the real world

Fast Sensing and Adaptive Actuation for Robust Legged Locomotion

Robust legged locomotion in complex terrain demands fast perturbation detection and reaction. In animals, due to the neural transmission delays, the high-level control loop involving the brain is absent from mitigating the initial disturbance. Instead, the low-level compliant behavior embedded in mechanics and the mid-level controllers in the spinal cord are believed to provide quick response during fast locomotion. Still, it remains unclear how these low- and mid-level components facilitate robust locomotion. This thesis aims to identify and characterize the underlining elements responsible for fast sensing and actuation. To test individual elements and their interplay, several robotic systems were implemented. The implementations include active and passive mechanisms as a combination of elasticities and dampers in multi-segment robot legs, central pattern generators inspired by intraspinal controllers, and a synthetic robotic version of an intraspinal sensor. The first contribution establishes the notion of effective damping. Effective damping is defined as the total energy dissipation during one step, which allows quantifying how much ground perturbation is mitigated. Using this framework, the optimal damper is identified as viscous and tunable. This study paves the way for integrating effective dampers to legged designs for robust locomotion. The second contribution introduces a novel series elastic actuation system. The proposed system tackles the issue of power transmission over multiple joints, while featuring intrinsic series elasticity. The design is tested on a hopper with two more elastic elements, demonstrating energy recuperation and enhanced dynamic performance. The third contribution proposes a novel tunable damper and reveals its influence on legged hopping. A bio-inspired slack tendon mechanism is implemented in parallel with a spring. The tunable damping is rigorously quantified on a central-pattern-generator-driven hopping robot, which reveals the trade-off between locomotion robustness and efficiency. The last contribution explores the intraspinal sensing hypothesis of birds. We speculate that the observed intraspinal structure functions as an accelerometer. This accelerometer could provide fast state feedback directly to the adjacent central pattern generator circuits, contributing to birds’ running robustness. A biophysical simulation framework is established, which provides new perspectives on the sensing mechanics of the system, including the influence of morphologies and material properties. Giving an overview of the hierarchical control architecture, this thesis investigates the fast sensing and actuation mechanisms in several control layers, including the low-level mechanical response and the mid-level intraspinal controllers. The contributions of this work provide new insight into animal loco-motion robustness and lays the foundation for future legged robot design

Design of Low-Cost Modular Bio-Inspired Electric–Pneumatic Actuator (EPA)-Driven Legged Robots

Exploring the fundamental mechanisms of locomotion extends beyond mere simulation and modeling. It necessitates the utilization of physical test benches to validate hypotheses regarding real-world applications of locomotion. This study introduces cost-effective modular robotic platforms designed specifically for investigating the intricacies of locomotion and control strategies. Expanding upon our prior research in electric–pneumatic actuation (EPA), we present the mechanical and electrical designs of the latest developments in the EPA robot series. These include EPA Jumper, a human-sized segmented monoped robot, and its extension EPA Walker, a human-sized bipedal robot. Both replicate the human weight and inertia distributions, featuring co-actuation through electrical motors and pneumatic artificial muscles. These low-cost modular platforms, with considerations for degrees of freedom and redundant actuation, (1) provide opportunities to study different locomotor subfunctions—stance, swing, and balance; (2) help investigate the role of actuation schemes in tasks such as hopping and walking; and (3) allow testing hypotheses regarding biological locomotors in real-world physical test benches

On the effects of variable leg-spring properties during hopping

Das Federmassemodell, auch spring-loaded inverted pendulum (SLIP), beschreibt die Schwerpunktsbewegung biologischer Laufsysteme. Dieses Modell bildet die Beine als lineare Federn mit konstanten Parametern ab. In biologischen Systemen können sich federartige Eigenschaften der Gliedmaßen jedoch zeitlich ändern. Daher wurde in der vorliegenden Arbeit untersucht, inwieweit Variationen der Federparameter während des Bodenkontaktes die Dynamik des Federmassemodells beeinflussen