Comparison of elastic configurations for energy efficient legged locomotion

Energy efficient locomotion with the amazing agility of humans and other animals remains a challenge for legged robots. Many existing joint mechanisms for legged robots use a serial configuration which gives compliance, however this may be sub-optimal for energy efficiency. This paper investigates the energy efficiency of legged joints for stationary jumping for three configurations of the elastic and actuator elements: series, parallel and without an elastic element. The key result is that significant energy savings are possible with a parallel configuration over the series and nonelastic configurations for the range of typical animal and robot properties: mass, stance duty and toe jump height. While there are large regions where the series arrangement is more energy efficient, these are outside typical duty cycles and will be affected by significant impact losses. The results are obtained by optimizing a set of equations to find the minimum energy losses for stationary jumping. The scripts to generate the results are available as open source software

Optimal Design Methods for Increasing Power Performance of Multiactuator Robotic Limbs

abstract: In order for assistive mobile robots to operate in the same environment as humans, they must be able to navigate the same obstacles as humans do. Many elements are required to do this: a powerful controller which can understand the obstacle, and power-dense actuators which will be able to achieve the necessary limb accelerations and output energies. Rapid growth in information technology has made complex controllers, and the devices which run them considerably light and cheap. The energy density of batteries, motors, and engines has not grown nearly as fast. This is problematic because biological systems are more agile, and more efficient than robotic systems. This dissertation introduces design methods which may be used optimize a multiactuator robotic limb's natural dynamics in an effort to reduce energy waste. These energy savings decrease the robot's cost of transport, and the weight of the required fuel storage system. To achieve this, an optimal design method, which allows the specialization of robot geometry, is introduced. In addition to optimal geometry design, a gearing optimization is presented which selects a gear ratio which minimizes the electrical power at the motor while considering the constraints of the motor. Furthermore, an efficient algorithm for the optimization of parallel stiffness elements in the robot is introduced. In addition to the optimal design tools introduced, the KiTy SP robotic limb structure is also presented. Which is a novel hybrid parallel-serial actuation method. This novel leg structure has many desirable attributes such as: three dimensional end-effector positioning, low mobile mass, compact form-factor, and a large workspace. We also show that the KiTy SP structure outperforms the classical, biologically-inspired serial limb structure.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201

System Identification of Bipedal Locomotion in Robots and Humans

The ability to perform a healthy walking gait can be altered in numerous cases due to gait disorder related pathologies. The latter could lead to partial or complete mobility loss, which affects the patients’ quality of life. Wearable exoskeletons and active prosthetics have been considered as a key component to remedy this mobility loss. The control of such devices knows numerous challenges that are yet to be addressed. As opposed to fixed trajectories control, real-time adaptive reference generation control is likely to provide the wearer with more intent control over the powered device. We propose a novel gait pattern generator for the control of such devices, taking advantage of the inter-joint coordination in the human gait. Our proposed method puts the user in the control loop as it maps the motion of healthy limbs to that of the affected one. To design such control strategy, it is critical to understand the dynamics behind bipedal walking. We begin by studying the simple compass gait walker. We examine the well-known Virtual Constraints method of controlling bipedal robots in the image of the compass gait. In addition, we provide both the mechanical and control design of an affordable research platform for bipedal dynamic walking. We then extend the concept of virtual constraints to human locomotion, where we investigate the accuracy of predicting lower limb joints angular position and velocity from the motion of the other limbs. Data from nine healthy subjects performing specific locomotion tasks were collected and are made available online. A successful prediction of the hip, knee, and ankle joints was achieved in different scenarios. It was also found that the motion of the cane alone has sufficient information to help predict good trajectories for the lower limb in stairs ascent. Better estimates were obtained using additional information from arm joints. We also explored the prediction of knee and ankle trajectories from the motion of the hip joints

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

REAL-TIME COMPUTER CONTROL OF A PROTOTYPE BIPEDAL SYSTEM

While much work in the area of robotics has attempted to replicate the power and agility of biological locomotion in a physical system, even the most impressive prototypes to date are functionally very simple in comparison to their biological counterparts. Biological systems particularly excel in their performance of dynamic maneuvers, such as a run or a jump. These maneuvers require explosive leg power coupled with sudden changes in trajectory. In mechanical systems, these requirements create the need for high-performance actuation and fast real-time control. Through a fusion of biologically inspired design and intelligent control strategies, current work aims to perform these types of maneuvers on a prototype biped robot named KURMET. As part of this research thrust, the goal of this work was to establish real-time control for the bipedal system. A distributed control system, that uses a cutting edge motion controller in conjunction with a Linux host computer, was developed to control these maneuvers. The resulting system provides on-board real-time control capable of 1~kHz servo rates over the biped's four actuators. A distributed control framework was developed to interface this foundational control system with the Linux host. This framework was then applied to produce state-based control strategies which have demonstrated a walk and a high-performance jump in hardware. While applied to these two complex movements, the control framework's modular design facilitates extension to a wide range of motions. Thus, this work has laid the foundation for a rich set of investigations into dynamic maneuvers for this platform.Grant No. IIS-0535098 from the National Science FoundationNo embarg

Robust and Economical Bipedal Locomotion

For bipedal robots to gain widespread use, significant improvements must be made in their energetic economy and robustness against falling. An increase in economy can increase their functional range, while a reduction in the rate of falling can reduce the need for human intervention. This dissertation explores novel concepts that improve these two goals in a fundamental manner. By centering on core ideas instead of direct application, these concepts are aimed at influencing a wide range of current and future legged robots. The presented work can be broken into five major contributions. The first extends our understanding of the energetic economy of series elastic walking robots. This investigation uses trajectory optimization to find energy-miminizing periodic motions for a realistic model of the walking robot RAMone. The energetically optimal motions for this model are shown to closely resemble human walking at low speeds, and as the speed increases, the motions switch abruptly to those resembling human running. The second contribution explores the energetic economy of the real robot RAMone. Here the model used in the previous investigation is shown to closely match reality. In addition, this investigation demonstrates a concrete example of a trade-off between energetic economy and robustness. The third contribution takes a step towards addressing this trade-off by deriving a robot constraint that guarantees safety against falling. Such a constraint can be used to remove considerations of robustness while conducting future investigations into economical robot motions. The approach is demonstrated using a simple compass-gait style walking model. The fourth contribution extends this safety constraint towards higher-dimensional walking models, using a combination of hybrid zero dynamics and sums-of-squares analysis. This is demonstrated by safely modifying the pitch of a 10 dimensional Rabbit model walking over flat terrain. The final contribution pushes the safety guarantee towards a broader set of walking behaviours, including rough terrain walking. Throughout this work, a range of models are used to reason about the economy and robustness of walking robots. These model-based methods allow control designers to move away from heuristics and tuning, and towards generalizable and reliable controllers. This is vital for walking robots to push further into the wild.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153459/1/nilssmit_1.pd

Maneuver Based Design of Passive Assist Devices for Active Joints.

This thesis describes a novel, general methodology for designing a Passive Assist Device (PAD) (e.g., spring) to augment an actuated system using optimization based on a known maneuver of the active system. Implementation of the PAD can result in an improvement in system performance with respect to efficiency, reliability, and/or safety. The methodology is experimentally demonstrated with a parallel, torsional spring designed to minimize energy consumption of a prototypical, single link UGV robot arm. The method is extended to series systems as well as dual PAD systems that contain both a series and a parallel component. We show that the proposed method is not limited to robot manipulator joints, can be applied to multi-DOF systems, and can be used to design PADs that are robust against variation in the maneuver. Furthermore, for certain situations a significant increase in performance can be realized if the maneuver is redesigned considering that a PAD will be added to the system. The addition of properly designed energy minimizing springs can lead to a decrease in energy consumption, as shown in various engineering examples, by as much as 60-80% while also improving reliability and/or safety.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/100033/1/wrbrown_1.pd

Feedback Control of a Bipedal Walker and Runner with Compliance.

This dissertation contributes to the theoretical foundations of robotic bipedal locomotion and advances the experimental state of the art as well. On the theoretical side, a mathematical formalism for designing provably stable, walking and running gaits in bipedal robots with compliance is presented. A key contribution is a novel method of force control in robots with compliance. The theoretical work is validated experimentally on MABEL, a planar bipedal testbed that contains springs in its drivetrain for the purpose of enhancing both energy efficiency and agility of dynamic locomotion. While the potential energetic benefits of springs are well documented in the literature, feedback control designs that effectively realize this potential are lacking. The methods of virtual constraints and hybrid zero dynamics, originally developed for rigid robots with a single degree of underactuation, are extended and applied to MABEL, which has a novel compliant transmission and multiple degrees of underactuation. A time-invariant feedback controller is designed such that the closed-loop system respects the natural compliance of the open-loop system and realizes exponentially stable walking gaits. A second time-invariant feedback controller is designed such that the closed-loop system not only respects the natural compliance of the open-loop system, but also enables active force control within the compliant hybrid zero dynamics and results in exponentially stable running gaits. Several experiments are presented that highlight different aspects of MABEL and the feedback design method, ranging from basic elements such as stable walking, robustness under perturbations, energy efficient walking to a bipedal robot walking speed record of 1.5 m/s (3.4 mph), stable running with passive feet and with point feet. On MABEL, the full hybrid zero dynamics controller is implemented and was instrumental in achieving rapid walking and running, leading upto a kneed bipedal running speed record of 3.06 m/s (6.8 mph).Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89801/1/koushils_1.pd