John R. Rebula

Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models

This two-part paper discusses the analysis and control of legged locomotion in terms of N-step capturability: the ability of a legged system to come to a stop without falling by taking N or fewer steps. We consider this ability to be crucial to legged locomotion and a useful, yet not overly restrictive criterion for stability. In this part (Part 1), we introduce a theoretical framework for assessing N-step capturability. This framework is used to analyze three simple models of legged locomotion. All three models are based on the 3D Linear Inverted Pendulum Model. The first model relies solely on a point foot step location to maintain balance, the second model adds a finite-sized foot, and the third model enables the use of centroidal angular momentum by adding a reaction mass. We analyze how these mechanisms influence N-step capturability, for any N > 0. Part 2 will show that these results can be used to control a humanoid robot.

Capturability-based analysis and control of legged locomotion, Part 2: Application to M2V2, a lower-body humanoid

This two-part paper discusses the analysis and control of legged locomotion in terms of N-step capturability: the ability of a legged system to come to a stop without falling by taking N or fewer steps. We consider this ability to be crucial to legged locomotion and a useful, yet not overly restrictive criterion for stability. Part 1 introduced the N-step capturability framework and showed how to obtain capture regions and control sequences for simplified gait models. In Part 2, we describe an algorithm that uses these results as approximations to control a humanoid robot. The main contributions of this part are (1) step location adjustment using the 1-step capture region, (2) novel instantaneous capture point control strategies, and 3) an experimental evaluation of the 1-step capturability margin. The presented algorithm was tested using M2V2, a 3D force-controlled bipedal robot with 12 actuated degrees of freedom in the legs, both in simulation and in physical experiments. The physical robot was able to recover from forward and sideways pushes of up to 21 Ns while balancing on one leg and stepping to regain balance. The simulated robot was able to recover from sideways pushes of up to 15 Ns while walking, and walked across randomly placed stepping stones.

Learning Capture Points for humanoid push recovery

We present a method for learning capture points for humanoid push recovery. A capture point is a point on the ground to which the biped can step and stop without requiring another step. Being able to predict the location of such points is very useful for recovery from significant disturbances, such as after being pushed. While dynamic models can be used to compute capture points, model assumptions and modeling errors can lead to stepping in the wrong place, which can result in large velocity errors after stepping.We present a method for computing capture points by learning offsets to the capture points predicted by the linear inverted pendulum model, which assumes a point mass biped with constant center of Mass height. We validate our method on a three dimensional humanoid robot simulation with 12 actuated lower body degrees of freedom, distributed mass, and articulated limbs. Using our learning approach, robustness to pushes is significantly improved as compared to using the linear inverted pendulum model without learning.

Measurement of foot placement and its variability with inertial sensors

Gait parameters such as stride length, width, and period, as well as their respective variabilities, are widely used as indicators of mobility and walking function. Foot placement and its variability have thus been applied in areas such as aging, fall risk, spinal cord injury, diabetic neuropathy, and neurological conditions. But a drawback is that these measures are presently best obtained with specialized laboratory equipment such as motion capture systems and instrumented walkways, which may not be available in many clinics and certainly not during daily activities. One alternative is to fix inertial measurement units (IMUs) to the feet or body to gather motion data. However, few existing methods measure foot placement directly, due to drift associated with inertial data. We developed a method to measure stride-to-stride foot placement in unconstrained environments, and tested whether it can accurately quantify gait parameters over long walking distances. The method uses ground contact conditions to correct for drift, and state estimation algorithms to improve estimation of angular orientation. We tested the method with healthy adults walking over-ground, averaging 93 steps per trial, using a mobile motion capture system to provide reference data. We found IMU estimates of mean stride length and duration within 1% of motion capture, and standard deviations of length and width within 4% of motion capture. Step width cannot be directly estimated by IMUs, although lateral stride variability can. Inertial sensors measure walks over arbitrary distances, yielding estimates with good statistical confidence. Gait can thus be measured in a variety of environments, and even applied to long-term monitoring of everyday walking.

The Yobotics-IHMC Lower Body Humanoid Robot

This video highlights work to date on the Yobotics-IHMC Lower Body Humanoid Robot. The robot is a twelve degree-of-freedom robot with force controllable Series Elastic Actuators at each degree of freedom. Control algorithms utilize Virtual Model Control, and foot placement is determined using Capture Regions. The robot can recover from moderate disturbances and walk on flat ground. Ongoing work is focused on improving robustness to disturbances, walking more quickly and efficiently, and walking over rough terrain.

The Cost of Leg Forces in Bipedal Locomotion: A Simple Optimization Study

Simple optimization models show that bipedal locomotion may largely be governed by the mechanical work performed by the legs, minimization of which can automatically discover walking and running gaits. Work minimization can reproduce broad aspects of human ground reaction forces, such as a double-peaked profile for walking and a single peak for running, but the predicted peaks are unrealistically high and impulsive compared to the much smoother forces produced by humans. The smoothness might be explained better by a cost for the force rather than work produced by the legs, but it is unclear what features of force might be most relevant. We therefore tested a generalized force cost that can penalize force amplitude or its n-th time derivative, raised to the p-th power (or p-norm), across a variety of combinations for n and p. A simple model shows that this generalized force cost only produces smoother, human-like forces if it penalizes the rate rather than amplitude of force production, and only in combination with a work cost. Such a combined objective reproduces the characteristic profiles of human walking (R 2 = 0.96) and running (R 2 = 0.92), more so than minimization of either work or force amplitude alone (R 2 = −0.79 and R 2 = 0.22, respectively, for walking). Humans might find it preferable to avoid rapid force production, which may be mechanically and physiologically costly.

Influence of contextual task constraints on preferred stride parameters and their variabilities during human walking.

Walking is not always a free and unencumbered task. Everyday activities such as walking in pairs, in groups, or on structured walkways can limit the acceptable gait patterns, leading to motor behavior that differs from that observed in more self-selected gait. Such different contexts may lead to gait performance different than observed in typical laboratory experiments, for example, during treadmill walking. We sought to systematically measure the impact of such task constraints by comparing gait parameters and their variability during walking in different conditions over-ground, and on a treadmill. We reconstructed foot motion from foot-mounted inertial sensors, and characterized forward, lateral and angular foot placement while subjects walked over-ground in a straight hallway and on a treadmill. Over-ground walking was performed in three variations: with no constraints (self-selected, SS); while deliberately varying walking speed (self-varied, SV); and while following a toy pace car programmed to vary speed (externally-varied, EV). We expected that these conditions would exhibit a statistically similar relationship between stride length and speed, and between stride length and stride period. We also expected treadmill walking (TM) would differ in two ways: first, that variability in stride length and stride period would conform to a constant-speed constraint opposite in slope from the normal relationship; and second, that stride length would decrease, leading to combinations of stride length and speed not observed in over-ground conditions. Results showed that all over-ground conditions used similar stride length-speed relationships, and that variability in treadmill walking conformed to a constant-speed constraint line, as expected. Decreased stride length was observed in both TM and EV conditions, suggesting adaptations due to heightened awareness or to prepare for unexpected changes or problems. We also evaluated stride variability in constrained and unconstrained tasks. We observed that in treadmill walking, lateral variability decreased while forward variability increased, and the normally-observed correlation between wider foot placement and external foot rotation was eliminated. Preferred stride parameters and their variability appear significantly influenced by the context and constraints of the walking task.

Mobile platform for motion capture of locomotion over long distances

Motion capture is usually performed on only a few steps of over-ground locomotion, limited by the finite sensing volume of most capture systems. This makes it difficult to evaluate walking over longer distances, or in a natural environment outside the laboratory. Here we show that motion capture may be performed relative to a mobile platform, such as a wheeled cart that is moved with the walking subject. To determine the persons absolute displacement in space, the carts own motion must be localized. We present three localization methods and evaluate their performance. The first detects cart motion solely from the relative motion of the subjects feet during walking. The others use sensed motion of the carts wheels to perform odometry, with and without an additional gyroscope to enhance sensitivity to turning about the vertical axis. We show that such methods are practical to implement, and with present-day sensors can yield accuracy of better than 1% over arbitrary distances.

The stabilizing properties of foot yaw in human walking

Humans perform a variety of feedback adjustments to maintain balance during walking. These include lateral footfall placement, and center of pressure adjustment under the stance foot, to stabilize lateral balance. A less appreciated possibility would be to steer for balance like a bicycle, whose front wheel may be turned toward the direction of a lean to capture the center of mass. Humans could potentially combine steering with other strategies to distribute balance adjustments across multiple degrees of freedom. We tested whether human balance can theoretically benefit from steering, and experimentally tested for evidence of steering for balance. We first developed a simple dynamic walking model, which shows that bipedal walking may indeed be stabilized through steering-externally rotating the foot about vertical toward the direction of lateral lean for each footfall-governed by linear feedback control. Moreover, least effort (mean-square control torque) is required if steering is combined with lateral foot placement. If humans use such control, footfall variability should show a statistical coupling between external rotation with lateral placement. We therefore examined the spontaneous fluctuations of hundreds of strides of normal overground walking in healthy adults (N=26). We found significant coupling (P=9·10-8), of 0.54rad of external rotation per meter of lateral foot deviation. Successive footfalls showed a weaker, negative correlation with each other, similar to how a bicycle׳s steering adjustment made for balance must be followed by gradual corrections to resume the original travel direction. Steering may be one of multiple strategies to stabilize balance during walking.

Learning terrain cost maps

We train the dog on several diverse terrains, progressively building up a database of good and bad points, along with their three characteristic parameters. The quality of a terrain point is determined by measuring the distance that the foot slips. We start by walking the LilttleDog on flat ground. The lower left visual shows the raw data being collected. In the lower right, we demonstrate how, as more data is collected, we are able to progressively generalize to an uncharted terrain.