Jonathan W. Hurst

An actuator with physically variable stiffness for highly dynamic legged locomotion

Running is a complex dynamical task which places strict design requirements on both the physical components and software control systems of a robot. This paper explores some of those requirements and illustrates how a variable compliance actuation system can satisfy them. We present the design, analysis, simulation, and benchtop experimental validation of such an actuator system. We demonstrate, through simulation, the application of our prototype actuator to the problem of biped running.

The Actuator With Mechanically Adjustable Series Compliance

Running is a complex dynamic task that places strict requirements on both the physical components and software-control systems of a robot. This paper explores some of those requirements and, in particular, explores how a variable-compliance actuation system can satisfy many of them. We present the mechanical design and software-control system for such an actuator system. We analyze its performance through simulation and bench-top experimental validation of a prototype version. In conclusion, we demonstrate, through simulation, the application of our proof-of-concept actuator to the problem of biped running.

MABEL, a new robotic bipedal walker and runner

This paper introduces MABEL, a new platform for the study of bipedal locomotion in robots. One of the purposes of building the mechanism is to explore a novel powertrain design that incorporates compliance, with the objective of improving the power efficiency of the robot, both in steady state operation and in responding to disturbances. A second purpose is to inspire the development of new feedback control algorithms for running on level surfaces and walking on rough terrain. A third motivation for building the robot is science and technology outreach; indeed, it is already included in tours when K-through-12 students visit the College of Engineering at the University of Michigan. MABEL is currently walking at 1.1 m/s on a level surface, and a related monopod at Carnegie Mellon is hopping well, establishing that the testbed has the potential to realize its many objectives.

Series compliance for an efficient running gait

The important message to take from this article is that a robot is a unified dynamic system comprising electronics, software, and mechanical components, and for certain tasks such as running, a significant portion of the behavior is best exhibited through natural dynamics of the mechanism. Therefore, the mechanical system must be specialized for the task and designed with the same care for dynamic control as the software control system. In constructing the ECD leg, we have attempted to follow this philosophy and design the mechanical system for the specific tasks of walking and running. The prototype actuator, with dynamics verified by testing, exhibited behavior that enabled running in simulation. The ECD leg builds on design revisions from the BiMASC prototype, and the successful experiments with Thumper hopping around the laboratory have proven the ideas and engineering behind the design. Prof. Grizzles group at the University of Michigan has already demonstrated tentative walking with MABEL, and we expect to demonstrate robust and efficient walking and running gaits in the near future.

Performance Analysis and Feedback Control of ATRIAS, A Three-Dimensional Bipedal Robot

This paper develops feedback controllers for walking in 3D, on level ground, with energy efficiency as the performance objective. Assume The Robot Is AS phere (ATRIAS) 2.1 is a new robot that has been designed for the study of 3D bipedal locomotion, with the aim of combining energy efficiency, speed, and robustness with respect to natural terrain variations in a single platform. The robot is highly underactuated, having 6 actuators and, in single support, 13 degrees of freedom. Its sagittal plane dynamics are designed to embody the spring loaded inverted pendulum (SLIP), which has been shown to provide a dynamic model of the body center of mass during steady running gaits of a wide diversity of terrestrial animals. A detailed dynamic model is used to optimize walking gaits with respect to the cost of mechanical transport (CMT), a dimensionless measure of energetic efficiency, for walking speeds ranging from 0.5 m=s ðÞ to 1.4 m=s

Identification of a Bipedal Robot with a Compliant Drivetrain

Research in bipedal robotics aims to design machines with the speed, stability, agility, and energetic efficiency of a human. While no machine built today realizes the union of these attributes, several robots demonstrate one or more of them. The Cornell biped is designed to be highly energy efficient.

Don't break a leg: running birds from quail to ostrich prioritise leg safety and economy on uneven terrain

Cursorial ground birds are paragons of bipedal running that span a 500-fold mass range from quail to ostrich. Here we investigate the task-level control priorities of cursorial birds by analysing how they negotiate single-step obstacles that create a conflict between body stability (attenuating deviations in body motion) and consistent leg force–length dynamics (for economy and leg safety). We also test the hypothesis that control priorities shift between body stability and leg safety with increasing body size, reflecting use of active control to overcome size-related challenges. Weight-support demands lead to a shift towards straighter legs and stiffer steady gait with increasing body size, but it remains unknown whether non-steady locomotor priorities diverge with size. We found that all measured species used a consistent obstacle negotiation strategy, involving unsteady body dynamics to minimise fluctuations in leg posture and loading across multiple steps, not directly prioritising body stability. Peak leg forces remained remarkably consistent across obstacle terrain, within 0.35 body weights of level running for obstacle heights from 0.1 to 0.5 times leg length. All species used similar stance leg actuation patterns, involving asymmetric force–length trajectories and posture-dependent actuation to add or remove energy depending on landing conditions. We present a simple stance leg model that explains key features of avian bipedal locomotion, and suggests economy as a key priority on both level and uneven terrain. We suggest that running ground birds target the closely coupled priorities of economy and leg safety as the direct imperatives of control, with adequate stability achieved through appropriately tuned intrinsic dynamics.

Dynamic multi-domain bipedal walking with atrias through SLIP based human-inspired control

This paper presents a methodology for achieving efficient multi-domain underactuated bipedal walking on compliant robots by formally emulating gaits produced by the Spring Loaded Inverted Pendulum (SLIP). With the goal of achieving locomotion that displays phases of double and single support, a hybrid system model is formulated that faithfully represents the full-order dynamics of a compliant walking robot. The SLIP model is used as a bases for constructing human-inspired controllers that yield a dimension reduction through the use of hybrid zero dynamics. This allows for the formulation of an optimization problem that produces hybrid zero dynamics that best represents a SLIP model walking gait, while simultaneously ensuring the proper reduction in dimensionality that can be utilized to produce stable periodic orbits, i.e., walking gaits. The end result is stable robotic walking in simulation and, when implemented on the compliant robot ATRIAS, experimentally realized dynamic multi-domain locomotion.

Bio-inspired swing leg control for spring-mass robots running on ground with unexpected height disturbance.

We proposed three swing leg control policies for spring-mass running robots, inspired by experimental data from our recent collaborative work on ground running birds. Previous investigations suggest that animals may prioritize injury avoidance and/or efficiency as their objective function during running rather than maintaining limit-cycle stability. Therefore, in this study we targeted structural capacity (maximum leg force to avoid damage) and efficiency as the main goals for our control policies, since these objective functions are crucial to reduce motor size and structure weight. Each proposed policy controls the leg angle as a function of time during flight phase such that its objective function during the subsequent stance phase is regulated. The three objective functions that are regulated in the control policies are (i) the leg peak force, (ii) the axial impulse, and (iii) the leg actuator work. It should be noted that each control policy regulates one single objective function. Surprisingly, all three swing leg control policies result in nearly identical subsequent stance phase dynamics. This implies that the implementation of any of the proposed control policies would satisfy both goals (damage avoidance and efficiency) at once. Furthermore, all three control policies require a surprisingly simple leg angle adjustment: leg retraction with constant angular acceleration.

ATRIAS: Design and validation of a tether-free 3D-capable spring-mass bipedal robot

ATRIAS is a human-scale 3D-capable bipedal robot designed to mechanically embody the spring-mass model for dynamic walking and running. To help bring the extensive work on this theoretical model further into practice, we present the design and validation of a spring-mass robot that can operate in real-world settings (i.e. off-tether and without planarizing restraints). We outline the mechanisms and design choices necessary to meet these specifications, particularly ATRIAS’ four-bar series-elastic leg design. We experimentally demonstrate the following robot capabilities, which are characteristics of the target model. 1) We present the robot’s physical capability for both grounded and aerial gaits, including planar walking and sustained hopping, while being more efficient than similarly gait-versatile bipeds. 2) The robot can be controlled by enforcing quantities derived from the simpler spring-mass model, such as leg angles and leg forces. 3) ATRIAS replicates the center-of-mass dynamics of human hopping and (novelly) walking, a key spring-mass model feature. Lastly, we present dynamically stable stepping in 3D without external support, demonstrating that this theoretical model has practical potential for real-world locomotion.