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The natural impedance, or dynamic relationship between force and motion, of a human operator can determine the stability of exoskeletons that use interaction-torque feedback to amplify human strength. While human impedance is typically modelled as a linear system, our experiments on a single-joint exoskeleton testbed involving 10 human subjects show evidence of nonlinear behavior: a low-frequency asymptotic phase for the dynamic stiffness of the human that is different than the expected zero, and an unexpectedly consistent damping ratio as the stiffness and inertia vary. To explain these observations, this paper considers a new frequency-domain model of the human joint dynamics featuring complex value stiffness comprising a real stiffness term and a hysteretic damping term. Using a statistical F-test we show that the hysteretic damping term is not only significant but is even more significant than the linear damping term. Further analysis reveals a linear trend linking hysteretic damping and the real part of the stiffness, which allows us to simplify the complex stiffness model down to a 1-parameter system. Then, we introduce and demonstrate a customizable fractional-order controller that exploits this hysteretic damping behavior to improve strength amplification bandwidth while maintaining stability, and explore a tuning approach which ensures that this stability property is robust to muscle co-contraction for each individual., Comment: 10 pages, 7 figures, 4 tables. arXiv admin note: text overlap with arXiv:1903.00704

Practical application of $\mathcal H_\infty$ robust control relies on the system identification of a valid model set, described by a linear system in feedback with a stable norm-bounded uncertainty. This model set should explain all possible (or at least all previously measured) behavior for the controlled plant. Such models can be viewed as norm-bounded inclusions in the frequency domain. This note introduces the “quadric inclusion program” that can identify inclusions from the input–output data as a convex problem. We prove several key properties of this algorithm and give a geometric interpretation for its behavior. While we stress that the inclusion fitting is outlier sensitive by design, we offer a method to mitigate the effect of measurement noise. We apply this method to robustly approximate the simulated frequency-domain data using orthonormal basis functions. The result compares favorably with a least squares approach that satisfies the same data inclusion requirements.

Whole-body operational space controllers (WBOSCs) are versatile and well suited for simultaneously controlling motion and force behaviors, which can enable sophisticated modes of locomotion and balance. In this paper, we formulate a WBOSC for point-foot bipeds with series-elastic actuators (SEA) and experiment with it using a teen-size SEA biped robot. Our main contributions are on devising a WBOSC strategy for point-foot bipedal robots, 2) formulating planning algorithms for achieving unsupported dynamic balancing on our point-foot biped robot and testing them using a WBOSC, and 3) formulating force feedback control of the internal forces—corresponding to the subset of contact forces that do not generate robot motions—to regulate contact interactions with the complex environment. We experimentally validate the efficacy of our new whole-body control and planning strategies via balancing over a disjointed terrain and attaining dynamic balance through continuous stepping without a mechanical support.

Human impedance parameters play an integral role in the dynamics of strength amplification exoskeletons. Many methods are used to estimate the stiffness of human muscles, but few are used to improve the performance of strength amplification controllers for these devices. We propose a compliance shaping amplification controller incorporating an accurate online human stiffness estimation from surface electromyography (sEMG) sensors and stretch sensors connected to the forearm and upper arm of the human. These sensor values along with exoskeleton position and velocity are used to train a random forest regression model that accurately predicts a person's stiffness despite varying movement, relaxation, and muscle co-contraction. Our model's accuracy is verified using experimental test data and the model is implemented into the compliance shaping controller. Ultimately we show that the online estimation of stiffness can improve the bandwidth and amplification of the controller while remaining robustly stable., 8 pages, 9 figures, Accepted for publication at the 2020 American Control Conference. Copyright IEEE 2020

In this paper, we consider the problem of verifying safety constraint satisfaction for single-input single-output systems with uncertain transfer function coefficients. We propose a new type of barrier function based on a vector norm. This type of barrier function has a measurable upper bound without full state availability. An identifier-based estimator allows an exact bound for the uncertainty-based component of the barrier function estimate. Assuming that the system is safe initially allows an exponentially decreasing bound on the error due to the estimator transient. Barrier function and estimator synthesis is proposed as two convex sub-problems, exploiting linear matrix inequalities. The barrier function controller combination is then used to construct a safety backup controller. And we demonstrate the system in a simulation of a 1 degree-of-freedom human-exoskeleton interaction., 6 pages, 5 figures. Accepted for publication at the 2020 American Control Conference. Copyright IEEE 2020

In this paper we consider a class of exoskeletons designed to amplify the strength of humans through feedback of sensed human-robot interactions and actuator forces. We define an amplification error signal based on a reference amplification rate, and design a linear feedback compensator to attenuate this error. Since the human operator is an integral part of the system, we design the compensator to be robust to both a realistic variation in human impedance and a large variation in load impedance. We demonstrate our strategy on a one-degree of freedom amplification exoskeleton connected to a human arm, following a three dimensional matrix of experimentation: slow or fast human motion; light or extreme exoskeleton load; and soft or clenched human arm impedances. We demonstrate that a slightly aggressive controller results in a borderline stable system---but only for soft human musculoeskeletal behavior and a heavy load. This class of exoskeleton systems is interesting because it can both amplify a human's interaction forces --- so long as the human contacts the environment through the exoskeleton --- and attenuate the operator's perception of the exoskeleton's reflected dynamics at frequencies within the bandwidth of the control., 8 pages, 12 figures, 4 tables. Accepted for publication at the 2019 American Control Conference. Copyright IEEE 2019

Exoskeletons which amplify the strength of their operators can enable heavy-duty manipulation of unknown objects. However, this type of behavior is difficult to accomplish; it requires the exoskeleton to sense and amplify the operator's interaction forces while remaining stable. But, the goals of amplification and robust stability when connected to the operator fundamentally conflict. As a solution, we introduce a design with a spring in series with the force sensitive cuff. This allows us to design an exoskeleton compliance behavior which is nominally passive, even with high amplification ratios. In practice, time delay and discrete time filters prevent our strategy from actually achieving passivity, but the designed compliance still makes the exoskeleton more robust to spring-like human behaviors. Our exoskeleton is actuated by a series elastic actuator (SEA), which introduces another spring into the system. We show that shaping the cuff compliance for the exoskeleton can be made into approximately the same problem as shaping the spring compliance of an SEA. We therefore introduce a feedback controller and gain tuning method which takes advantage of an existing compliance shaping technique for SEAs. We call our strategy the "double compliance shaping" method. With large amplification ratios, this controller tends to amplify nonlinear transmission friction effects, so we additionally propose a "transmission disturbance observer" to mitigate this drawback. Our methods are validated on a single-degree-of-freedom elbow exoskeleton., Comment: 8 pages, 9 figures, conference

Human joint dynamic stiffness plays an important role in the stability of performance augmentation exoskeletons. In this paper, we consider a new frequency domain model of the human joint dynamics which features a complex value stiffness. This complex stiffness consists of a real stiffness and a hysteretic damping. We use it to explain the dynamic behaviors of the human connected to the exoskeleton, in particular the observed non-zero low frequency phase shift and the near constant damping ratio of the resonant as stiffness and inertia vary. We validate this concept by experimenting with an elbow-joint exoskeleton testbed on a subject while modifying joint stiffness behavior, exoskeleton inertia, and strength augmentation gains. We compare three different models of elbow-joint dynamic stiffness: a model with real stiffness, viscous damping and inertia, a model with complex stiffness and inertia, and a model combining the previous two models. Our results show that the hysteretic damping term improves modeling accuracy, using a statistical F-test. Moreover this improvement is statistically more significant than using classical viscous damping term. In addition, we experimentally observe a linear relationship between the hysteretic damping and the real part of the stiffness which allows us to simplify the complex stiffness model as a 1-parameter system. Ultimately, we design a fractional order controller to demonstrate how human hysteretic damping behavior can be exploited to improve strength amplification performance while maintaining stability., Comment: Accepted for publication in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Copyright 2019 IEEE

We introduce a hybrid (discrete--continuous) safety controller which enforces strict state and input constraints on a system---but only acts when necessary, preserving transparent operation of the original system within some safe region of the state space. We define this space using a Min-Quadratic Barrier function, which we construct along the equilibrium manifold using the Lyapunov functions which result from linear matrix inequality controller synthesis for locally valid uncertain linearizations. We also introduce the concept of a barrier pair, which makes it easy to extend the approach to include trajectory-based augmentations to the safe region, in the style of LQR-Trees. We demonstrate our controller and barrier pair synthesis method in simulation-based examples., Comment: 6 pages, 7 figures. Accepted for publication at the 2018 American Controls Conference. Copyright IEEE 2018

Series elastic robots are best able to follow trajectories which obey the limitations of their actuators, since they cannot instantly change their joint forces. In fact, the performance of series elastic actuators can surpass that of ideal force source actuators by storing and releasing energy. In this paper, we formulate the trajectory optimization problem for series elastic robots in a novel way based on sequential linear programming. Our framework is unique in the separation of the actuator dynamics from the rest of the dynamics, and in the use of a tunable pseudo-mass parameter that improves the discretization accuracy of our approach. The actuator dynamics are truly linear, which allows them to be excluded from trust-region mechanics. This causes our algorithm to have similar run times with and without the actuator dynamics. We demonstrate our optimization algorithm by tuning high performance behaviors for a single-leg robot in simulation and on hardware for a single degree-of-freedom actuator testbed. The results show that compliance allows for faster motions and takes a similar amount of computation time.

This paper presents a momentum-based control framework for floating-base robots and its application to the humanoid robot “Atlas”. At the heart of the control framework lies a quadratic program that reconciles motion tasks expressed as constraints on the joint acceleration vector with the limitations due to unilateral ground contact and force-limited grasping. We elaborate on necessary adaptations required to move from simulation to real hardware and present results for walking across rough terrain, basic manipulation, and multi-contact balancing on sloped surfaces (the latter in simulation only). The presented control framework was used to secure second place in both the DARPA Robotics Challenge Trials in December 2013 and the Finals in June 2015.

The small-signal impedance between the electrodes of an ionisation chamber is studied over a range of frequency and ionisation. The impedance is approximately that of an equivalent circuit which has one RC combination for each group of ions in the chamber. More accurate formulas are given. Experimental results support the theory.