C. David Remy

Stability Analysis of Passive Dynamic Walking of Quadrupeds

We introduce a detailed numerical simulation and analysis framework to extend the principles of passive dynamic walking to quadrupedal locomotion. Non-linear limit cycle methods are used to identify possible gaits and to analyze the stability and efficiency of quadrupedal passive dynamic walking. In doing so, special attention is paid to issues that are inherent to quadrupedal locomotion, such as the occurrence of simultaneous contact collisions and the implications of the phase difference between front and back leg pairs. Limit cycles identified within this framework correspond to periodic gaits and can be placed into two categories: in-phase gaits in which front and back legs hit the ground at roughly the same time, and out-of-phase gaits with a ±90° phase shift between the back and front leg pairs. The latter are, in comparison, energetically more efficient but exhibit one unstable eigenvalue that leads to a phase divergence and results in a gait-transition to a less efficient in-phase gait. A detailed analysis examines the influence of various parameters on stability and locomotion speed, with the ultimate goal of determining a stable solution for the energy-efficient, out-of-phase gait. This was achieved through the use of a wobbling mass, i.e. an additional mass that is elastically attached to the main body of the quadruped. The methods, results, and gaits presented in this paper additionally provide a point of departure for the exploration of the considerably richer range of quadrupedal locomotion found in nature.

Haptic terrain classification for legged robots

In this paper, we are presenting a method to estimate terrain properties (such as small-scale geometry or surface friction) to improve the assessment of stability and the guiding of foot placement of legged robots in rough terrain. Haptic feedback, expressed through joint motor currents and ground contact force measurements that arises when prescribing a predefined motion was collected for a variety of ground samples (four different shapes and four different surface properties). Features were extracted from this data and used for training and classification by a multiclass AdaBoost machine learning algorithm. In a single leg testbed, the algorithm could correctly classify about 94% of the terrain shapes, and about 73% of the surface samples.

SLIP running with an articulated robotic leg

SLIP models are generally known as one of the best and simplest abstractions describing the spring-like leg behavior found in human and animal running, and have thus been subject to exhaustive investigation. To exploit these findings in real robots, we utilize an operational space controller that projects the behavior of the SLIP model onto the dynamics of an actual segmented robotic leg. Additionally, we introduce a method to compensate for the energetic losses at the impact collisions, which are not accounted for in the simplified SLIP assumptions. This allows the direct application of existing dead-beat control strategies to arbitrary robotic legs, for which we can show that the collision and compensation effects in the actual leg enlarge the regions of stable running and reduce the minimally required locomotion speed. The necessary joint torque profiles can be generated in large part passively, for example by using high compliance series elastic actuators.

Learning to walk with an adaptive gain proportional myoelectric controller for a robotic ankle exoskeleton

BackgroundRobotic ankle exoskeletons can provide assistance to users and reduce metabolic power during walking. Our research group has investigated the use of proportional myoelectric control for controlling robotic ankle exoskeletons. Previously, these controllers have relied on a constant gain to map user’s muscle activity to actuation control signals. A constant gain may act as a constraint on the user, so we designed a controller that dynamically adapts the gain to the user’s myoelectric amplitude. We hypothesized that an adaptive gain proportional myoelectric controller would reduce metabolic energy expenditure compared to walking with the ankle exoskeleton unpowered because users could choose their preferred control gain.MethodsWe tested eight healthy subjects walking with the adaptive gain proportional myoelectric controller with bilateral ankle exoskeletons. The adaptive gain was updated each stride such that on average the user’s peak muscle activity was mapped to maximal power output of the exoskeleton. All subjects participated in three identical training sessions where they walked on a treadmill for 50 minutes (30 minutes of which the exoskeleton was powered) at 1.2 ms-1. We calculated and analyzed metabolic energy consumption, muscle recruitment, inverse kinematics, inverse dynamics, and exoskeleton mechanics.ResultsUsing our controller, subjects achieved a metabolic reduction similar to that seen in previous work in about a third of the training time. The resulting controller gain was lower than that seen in previous work (β=1.50±0.14 versus a constant β=2). The adapted gain allowed users more total ankle joint power than that of unassisted walking, increasing ankle power in exchange for a decrease in hip power.ConclusionsOur findings indicate that humans prefer to walk with greater ankle mechanical power output than their unassisted gait when provided with an ankle exoskeleton using an adaptive controller. This suggests that robotic assistance from an exoskeleton can allow humans to adopt gait patterns different from their normal choices for locomotion. In our specific experiment, subjects increased ankle power and decreased hip power to walk with a reduction in metabolic cost. Future exoskeleton devices that rely on proportional myolectric control are likely to demonstrate improved performance by including an adaptive gain.

Optimal Estimation of Dynamically Consistent Kinematics and Kinetics for Forward Dynamic Simulation of Gait

Forward dynamic simulation provides a powerful framework for characterizing internal loads and for predicting changes in movement due to injury, impairment or surgical intervention. However, the computational challenge of generating simulations has greatly limited the use and application of forward dynamic models for simulating human gait. In this study, we introduce an optimal estimation approach to efficiently solve for generalized accelerations that satisfy the overall equations of motion and best agree with measured kinematics and ground reaction forces. The estimated accelerations are numerically integrated to enforce dynamic consistency over time, resulting in a forward dynamic simulation. Numerical optimization is then used to determine a set of initial generalized coordinates and speeds that produce a simulation that is most consistent with the measured motion over a full cycle of gait. The proposed method was evaluated with synthetically created kinematics and force plate data in which both random noise and bias errors were introduced. We also applied the method to experimental gait data collected from five young healthy adults walking at a preferred speed. We show that the proposed residual elimination algorithm (REA) converges to an accurate solution, reduces the detrimental effects of kinematic measurement errors on joint moments, and eliminates the need for residual forces that arise in standard inverse dynamics. The greatest improvements in joint kinetics were observed proximally, with the algorithm reducing joint moment errors due to marker noise by over 20% at the hip and over 50% at the low back. Simulated joint angles were generally within 1 deg of recorded values when REA was used to generate a simulation from experimental gait data. REA can thus be used as a basis for generating accurate simulations of subject-specific gait dynamics.

Walking and crawling with ALoF: a robot for autonomous locomotion on four legs

Purpose - The purpose of this paper is to introduce the robotic quadrupedal platform ALoF that is designed to aid research on perception in legged locomotion. Design/methodology/approach - A well-balanced size and complexity of the robot results in a robust platform that is easy to handle, yet able to perform complex maneuvers as well as to carry sophisticated 3D sensors. A very large range of motion allows the robot to actively explore its surroundings through haptic interaction, and to choose between a wide range of planning options. Findings - This robot was employed and tested in the lunar robotics challenge organized by the European Space Agency, for which the authors also developed a novel crawling gait, in which the weight of the robot is alternately supported by scaled plates under the main body and the four shank segments. This allowed for stable locomotion in steep terrain with very loose soil. Originality/value - The paper describes how a very large range of motion allows the robot to actively explore its surroundings through haptic interaction, and to choose between a wide range of planning options. The paper describes how the authors developed a novel crawling gait, in which the weight of the robot is alternately supported by scaled plates under the main body and the four shank segments.

Body-In-The-Loop: Optimizing Device Parameters Using Measures of Instantaneous Energetic Cost

This paper demonstrates methods for the online optimization of assistive robotic devices such as powered prostheses, orthoses and exoskeletons. Our algorithms estimate the value of a physiological objective in real-time (with a body “in-the-loop”) and use this information to identify optimal device parameters. To handle sensor data that are noisy and dynamically delayed, we rely on a combination of dynamic estimation and response surface identification. We evaluated three algorithms (Steady-State Cost Mapping, Instantaneous Cost Mapping, and Instantaneous Cost Gradient Search) with eight healthy human subjects. Steady-State Cost Mapping is an established technique that fits a cubic polynomial to averages of steady-state measures at different parameter settings. The optimal parameter value is determined from the polynomial fit. Using a continuous sweep over a range of parameters and taking into account measurement dynamics, Instantaneous Cost Mapping identifies a cubic polynomial more quickly. Instantaneous Cost Gradient Search uses a similar technique to iteratively approach the optimal parameter value using estimates of the local gradient. To evaluate these methods in a simple and repeatable way, we prescribed step frequency via a metronome and optimized this frequency to minimize metabolic energetic cost. This use of step frequency allows a comparison of our results to established techniques and enables others to replicate our methods. Our results show that all three methods achieve similar accuracy in estimating optimal step frequency. For all methods, the average error between the predicted minima and the subjects’ preferred step frequencies was less than 1% with a standard deviation between 4% and 5%. Using Instantaneous Cost Mapping, we were able to reduce subject walking-time from over an hour to less than 10 minutes. While, for a single parameter, the Instantaneous Cost Gradient Search is not much faster than Steady-State Cost Mapping, the Instantaneous Cost Gradient Search extends favorably to multi-dimensional parameter spaces.

Contraction Sensing With Smart Braid McKibben Muscles

The inherent compliance of soft fluidic actuators makes them attractive for use in wearable devices and soft robotics. Their flexible nature permits them to be used without traditional rotational or prismatic joints. Without these joints, however, measuring the motion of the actuators is challenging. Actuator-level sensors could improve the performance of continuum robots and robots with compliant or multi-degree-of-freedom joints. We make the reinforcing braid of a pneumatic artificial muscle (PAM or McKibben muscle) “smart” by weaving it from conductive insulated wires. These wires form a solenoid-like circuit with an inductance that more than doubles over the PAM contraction. The reinforcing and sensing fibers can be used to measure the contraction of a PAM actuator with a simple linear function of the measured inductance, whereas other proposed self-sensing techniques rely on the addition of special elastomers or transducers, the technique presented in this paper can be implemented without modifications of this kind. We present and experimentally validate two models for Smart Braid sensors based on the long solenoid approximation and the Neumann formula, respectively. We test a McKibben muscle made from a Smart Braid in quasi-static conditions with various end loads and in dynamic conditions. We also test the performance of the Smart Braid sensor alongside steel.

Computational techniques for using insole pressure sensors to analyse three-dimensional joint kinetics

This study evaluated the feasibility of using insole pressure sensors together with whole body dynamics to analyse joint kinetics while running. Local affine transformations of shoe kinematics were first used to track the position of insole sensors during locomotion. Centre of pressure estimates derived from the insoles were within 10 mm of forceplate measures through much of stance, while vertical force estimates were within 15% of peak forceplate recordings. Insole data were then coupled with a least squares whole body dynamic model to obtain shear force estimates that were comparable to forceplate records during running. We demonstrated that these techniques provide a viable approach for analysing joint kinetics when running on uninstrumented surfaces.

Design of an articulated robotic leg with nonlinear series elastic actuation

An articulated leg for the use in a running robot is presented. It is driven by series elastic actuation with a highly compliant spring at the knee joint to exploit periodic energy storage and passively support a running motion. The spring is connected with the knee motor by a cable pulley system, which allows the advantageous placement of the motor in the hip joint and enables us to use a compression spring instead of a heavier torsional element. Additionally, the pulley system creates a nonlinear spring characteristic at joint level which can be shaped by altering the cable tension. This nonlinearity and the inertial effects associated with it substantially increase the effective damping in the unloaded leg and allow precise foot-placement during the flight phase. Still, damping of the loaded leg during stance phase is kept minimal for highly efficient energy recovery.