Gray C. Thomas

Binghan He, Gray C. Thomas, Nicholas Paine et al.

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.

Gray C. Thomas, Binghan He, Luis Sentis

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.

Gray C. Thomas, Luis Sentis

Practical application of H[infinity] robust control relies on system identification of a valid model-set, described by a linear system in feedback with a stable norm-bounded uncertainty, which must explains all possible (or at least all previously measured) behavior for the control plant. Such models can be viewed as norm-bounded inclusions in the frequency domain, and this note introduces the "Quadric Inclusion Program" that can identify inclusions from 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 simulated frequency domain data using orthonormal basis functions. The result compares favorably with a least squares approach that satisfies the same data inclusion requirements.

Binghan He, Huang Huang, Gray C. Thomas et al.

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.

Binghan He, Huang Huang, Gray C. Thomas et al.

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.

Rachel Schlossman, Gray C. Thomas, Orion Campbell et al.

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.