An Efficiently Solvable Quadratic Program for Stabilizing Dynamic Locomotion

We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while respecting the dynamic, input, and contact constraints of the full robot dynamics. By exploiting sparsity and temporal structure in the optimization with a custom active-set algorithm, we surpass the performance of the best available off-the-shelf solvers and achieve 1kHz control rates for a 34-DOF humanoid. We describe applications to balancing and walking tasks using the simulated Atlas robot in the DARPA Virtual Robotics Challenge.Comment: 6 pages, published at ICRA 201

Kinematic Basis for Body Specific Locomotor Mechanics and Perturbation Responses

Animals have evolved mechanical and neural strategies for locomotion in almost every environment, overcoming the complexities of their habitats using specializations in body structure and animal behavior. These specializations are created by neural networks responsible for generating and altering muscle activation. Species specific musculoskeletal anatomy and physiology determine how locomotion is controlled through the transformation of motor patterns into body movements. Furthermore, when these species specific locomotor systems encounter perturbations during running and walking their behavioral and mechanical attributes determine how stability is established during and after the perturbation. It is still not understood how species specific structural and behavioral variables contribute to locomotion in non-uniform environments. To understand how these locomotor properties produce unique gaits and stability strategies we compared three species of brachyuran crabs during normal and perturbed running. Although all crabs ran sideways, morphological and kinematic differences explained how each species produced its unique gait and stability response. Despite the differences in running behavior and perturbation response, animals tended to use locomotor resources that were in abundance during stabilizing responses. Each crab regained stability during the perturbation response by altering leg joint movements or harnessing the body\u27s momentum. These species body designs and running behavior show how slight changes in body structure and joint kinematics can produce locomotor systems with unique mechanical profiles and abilities. Understanding how evolutionary pressures have optimized animals\u27 locomotor ability to successfully move in different environments will provide a deeper understanding of how to mimic these movements through mathematical models and robotics

Impedance control for legged robots: an insight into the concepts involved

The application of impedance control strategies to modern legged locomotion is analyzed, paying special attention to the concepts behind its implementation which is not straightforward. In order to implement a functional impedance controller for a walking mechanism, the concepts of contact, impact, friction, and impedance have to be merged together. A literature review and a comprehensive analysis are presented compiling all these concepts along with a discussion on position-based versus force-based impedance control approaches, and a theoretical model of a robotic leg in contact with its environment is introduced. A theoretical control scheme for the legs of a general legged robot is also introduced, and some simulations results are presented

The landscape of movement control in locomotion: Cost, strategy, and solution

Features of gait are determined at multiple levels, from the selection of the gait itself (e.g., walk or run) through the specific parameters utilized (stride length, frequency, etc.) to the pattern of muscular excitation. The ultimate choices are determined neurally, but what is involved with deciding on the appropriate strategy? Human locomotion appears stereotyped not so much because the pattern is predetermined, but because these movement patterns are good solutions for providing movement utilizing the machinery available to the individual (the legs and their requisite components). Under different circumstances the appropriate solution may differ broadly (different gait) or subtly (different parameters). Interpretation of the neural decision making process would benefit from understanding the influences that are utilized in the selection of the appropriate solution in any set of circumstances, including normal conditions. In this review we survey an array of studies that point to energetic cost as a key input to the gait coordination system, and not just an outcome of the gait pattern implemented. We then use that information to rigorously define the construct proposed by Sparrow and Newell (1998) where the effects of environment, organism, and task act as constraints determining the solution set available, and the coordination pattern is then implemented under pressure for energetic economy. The fit between the environment and the organism define affordances that can be actualized. We rely on a novel conceptualization of task that recognizes that the task goal needs to be separated from the mechanisms that achieve it so that the selection of a particular implementation strategy can be exposed and understood. This reformulation of the Sparrow and Newell construct is then linked to the proposed pressure for economy by considering it as an optimization problem, where the most readily selected gait strategy will be the one that achieves the task goal at (or near) the energetic minimum

Effects of Hip and Ankle Moments on Running Stability: Simulation of a Simplified Model

In human running, the ankle, knee, and hip moments are known to play different roles to influence the dynamics of locomotion. A recent study of hip moments and several hip-based legged robots have revealed that hip actuation can significantly improve the stability of locomotion, whether controlled or uncontrolled. Ankle moments are expected to also significantly affect running stability, but in a different way than hip moments. Here we seek to advance the current theory of dynamic running and associated legged robots by determining how simple open-loop ankle moments could affect running stability. We simulate a dynamical model, and compare it with a previous study on the role of hip moments. The model is relatively simple with a rigid trunk and a springy leg to represent the effective stiffness of the knee. At the hip we use a previously established proportional and derivative controlled moment with pitching angle as feedback. At the ankle we use the simplest ankle actuation, a constant ankle torque as a rough approximation of the net positive work done by the ankle moment during human locomotion. Even in this simplified model, we find that ankle and hip moments can affect the center of mass (COM) and pitching dynamics in distinct ways. Analysis of the governing equations shows that hip moments can directly influence the upper body balance, as well as indirectly influence the center of mass translation dynamics. However, ankle moments can only indirectly influence both. Simulation of the governing equations shows that the addition of ankle moment has significant benefits to the quality of locomotion stability, such as a larger basin of attraction. We also find that adding the ankle moments generally expands the range of parameters and velocities for which the model displays stable solutions. Overall, these findings suggest that ankle moments would play a significant role in improving the quality and range of running stability in a system with a rigid trunk and a telescoping leg, which would be a natural extension of current springy leg robots. Further, these results provide insights into the role that ankle moments might play in human locomotion

Gait Dynamic Stability Analysis with Wearable Assistive Robots

abstract: Lower-limb wearable assistive robots could alter the users gait kinematics by inputting external power, which can be interpreted as mechanical perturbation to subject normal gait. The change in kinematics may affect the dynamic stability. This work attempts to understand the effects of different physical assistance from these robots on the gait dynamic stability. A knee exoskeleton and ankle assistive device (Robotic Shoe) are developed and used to provide walking assistance. The knee exoskeleton provides personalized knee joint assistive torque during the stance phase. The robotic shoe is a light-weighted mechanism that can store the potential energy at heel strike and release it by using an active locking mechanism at the terminal stance phase to provide push-up ankle torque and assist the toe-off. Lower-limb Kinematic time series data are collected for subjects wearing these devices in the passive and active mode. The changes of kinematics with and without these devices on lower-limb motion are first studied. Orbital stability, as one of the commonly used measure to quantify gait stability through calculating Floquet Multipliers (FM), is employed to asses the effects of these wearable devices on gait stability. It is shown that wearing the passive knee exoskeleton causes less orbitally stable gait for users, while the knee joint active assistance improves the orbital stability compared to passive mode. The robotic shoe only affects the targeted joint (right ankle) kinematics, and wearing the passive mechanism significantly increases the ankle joint FM values, which indicates less walking orbital stability. More analysis is done on a mechanically perturbed walking public data set, to show that orbital stability can quantify the effects of external mechanical perturbation on gait dynamic stability. This method can further be used as a control design tool to ensure gait stability for users of lower-limb assistive devices.Dissertation/ThesisMasters Thesis Mechanical Engineering 201

Balance responses to lateral perturbations in human treadmill walking

During walking on a treadmill 10 human subjects (mean age 20 years) were perturbed by 100 ms pushes or pulls to the left or the right, of various magnitudes and in various phases of the gait cycle. Balance was maintained by (1) a stepping strategy (synergy), in which the foot at the next step is positioned a fixed distance outward of the 'extrapolated centre of mass', and (2) a lateral ankle strategy, which comprises a medial or lateral movement of the centre of pressure under the foot sole. The extrapolated centre of mass is defined as the centre of mass position plus the centre of mass velocity multiplied by a parameter related to the subject's leg length. The ankle strategy is the fastest, with a mechanical delay of about 200 ms (20% of a stride), but it can displace the centre of pressure no more than 2 cm. The stepping strategy needs at least 300 ms (30% of a stride) before foot placement, but has a range of 20 cm. When reaction time is sufficient, the magnitude of the total response is in good agreement with our hypothesis: mean centre of pressure (foot) position is a constant distance outward of the extrapolated centre of mass. If the reaction time falls short, a further correction is applied in the next step. In the healthy subjects studied here, no further corrections were necessary, so balance was recovered within two steps (one stride)

The Landscape of Movement Control in Locomotion: Cost, Strategy, and Solution

Features of gait are determined at multiple levels, from the selection of the gait itself (e.g., walk or run) through the specific parameters utilized (stride length, frequency, etc.) to the pattern of muscular excitation. The ultimate choices are determined neurally, but what is involved with deciding on the appropriate strategy? Human locomotion appears stereotyped not so much because the pattern is predetermined, but because these movement patterns are good solutions for providing movement utilizing the machinery available to the individual (the legs and their requisite components). Under different circumstances the appropriate solution may differ broadly (different gait) or subtly (different parameters). Interpretation of the neural decision making process would benefit from understanding the influences that are utilized in the selection of the appropriate solution in any set of circumstances, including normal conditions. In this review we survey an array of studies that point to energetic cost as a key input to the gait coordination system, and not just an outcome of the gait pattern implemented. We then use that information to rigorously define the construct proposed by Sparrow and Newell (1998) where the effects of environment, organism, and task act as constraints determining the solution set available, and the coordination pattern is then implemented under pressure for energetic economy. The fit between the environment and the organism define affordances that can be actualized. We rely on a novel conceptualization of task that recognizes that the task goal needs to be separated from the mechanisms that achieve it so that the selection of a particular implementation strategy can be exposed and understood. This reformulation of the Sparrow and Newell construct is then linked to the proposed pressure for economy by considering it as an optimization problem, where the most readily selected gait strategy will be the one that achieves the task goal at (or near) the energetic minimum