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Recent experiments have shown that human joints can maintain a constant damping ratio across a wide range of external loads. This behavior can be explained by the use of a “complex stiffness” frequency-domain model approximating the impedance of the human joint. However, for a robot to replicate this naturally beneficial human behavior would require a time-domain model of this nonlinear joint impedance. This letter demonstrates that there exists a nonlinear time-domain model (originally from the structural mechanics community) that has a frequency-domain “describing function” that matches the complex stiffness model observed in humans. We provide an extension of this nonlinear time-domain model that removes the need to implement hard-switching control input. In addition, we demonstrate that this proportional-and-hysteretic-damping controller has inertia-invariant overshoot and therefore offers an advantage over the more common proportional-derivative control approach. Implementing the proposed proportional-and-hysteretic-damping control in a single-joint test-robot, we demonstrate for the first time that the desired frequency domain behavior can be reproduced in practice.

While assistive exoskeletons typically focus on the metric of metabolic cost, we hypothesize that exoskeletons of sufficient power density could also reduce knee joint loading, which is understood to be a risk factor for osteoarthritis. Using biomechanical locomotion data, we run a simple simulation of two types of exoskeletons: those that provide a parallel load-path to ground, and those that apply torque directly to the human knee joint. We find that the second type offers larger reductions at normal walking speeds and that the power density required for knee load reduction is much lower than for metabolic cost reduction.

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.