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Behind any complex system in nature or engineering, there is an intricate network of interconnections that is often unknown. Using a control-theoretical approach, we study the problem of network reconstruction (NR): inferring both the network structure and the coupling weights based on measurements of each node's activity. We derive two new methods for NR, a low-complexity reduced-order estimator (which projects each node's dynamics to a one-dimensional space) and a full-order estimator for cases where a reduced-order estimator is not applicable. We prove their convergence to the correct network structure using Lyapunov-like theorems and persistency of excitation. Importantly, these estimators apply to systems with partial state measurements, a broad class of node dynamics and internode coupling functions, and in the case of the reduced-order estimator, node dynamics and internode coupling functions that are not fully known. The effectiveness of the estimators is illustrated using both numerical and experimental results on networks of chaotic oscillators.

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We present a method to identify the dynamics of a human arm controlled by an implanted functional electrical stimulation neuroprosthesis. The method uses Gaussian process regression to predict shoulder and elbow torques given the shoulder and elbow joint positions and velocities and the electrical stimulation inputs to muscles. We compare the accuracy of torque predictions of nonparametric, semiparametric, and parametric model types. The most accurate of the three model types is a semiparametric Gaussian process model that combines the flexibility of a black box function approximator with the generalization power of a parameterized model. The semiparametric model predicted torques during stimulation of multiple muscles with errors less than 20% of the total muscle torque and passive torque needed to drive the arm. The identified model allows us to define an arbitrary reaching trajectory and approximately determine the muscle stimulations required to drive the arm along that trajectory.

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We present a method for controlling a neuroprosthesis for a paralyzed human arm using functional electrical stimulation (FES) and characterize the errors of the controller. The subject has surgically implanted electrodes for stimulating muscles in her shoulder and arm. Using input/output data, a model mapping muscle stimulations to isometric endpoint forces measured at the subject's hand was identified. We inverted the model of this redundant and coupled multiple-input multiple-output system by minimizing muscle activations and used this inverse for feedforward control. The magnitude of the total root mean square error over a grid in the volume of achievable isometric endpoint force targets was 11% of the total range of achievable forces. Major sources of error were random error due to trial-to-trial variability and model bias due to nonstationary system properties. Because the muscles working collectively are the actuators of the skeletal system, the quantification of errors in force control guides designs of motion controllers for multi-joint, multi-muscle FES systems that can achieve arbitrary goals.

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Functional electrical stimulation (FES) can be used to restore movement control following paralysis. For complex multijoint systems, it is becoming increasingly apparent that closed-loop controllers are needed. Designing a closed-loop control system is easiest when the open-loop system is stable. In this study we developed a computational model to assess the open-loop stability of FES-control systems. We used the model to examine the open-loop stability of the human arm throughout its reachable workspace. For each simulated position of the hand we examined the stability of the arm, assuming that a minimal pattern of muscle activation was used to support the arm against gravity. Only muscles available to an existing FES user were considered. We found that with this reduced muscle set, the stability of the arm was severely compromised. We also demonstrated that muscle co-contraction can be an effective method to improve the stability for many postures.

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Weakly electric knifefish have intrigued both biologists and engineers for decades with their unique electrosensory system and agile swimming mechanics. Study of these fish has resulted in models that illuminate the principles behind their electrosensory system and unique swimming abilities. These models have uncovered the mechanisms by which knifefish generate thrust for swimming forward and backward, hovering, and heaving dorsally using a ventral elongated median fin. Engineered active electrosensory models inspired by electric fish allow for close-range sensing in turbid waters where other sensing modalities fail. Artificial electrosense is capable of aiding navigation, detection and discrimination of objects, and mapping the environment, all tasks for which the fish use electrosense extensively. While robotic ribbon fin and artificial electrosense research has been pursued separately to reduce complications that arise when they are combined, electric fish have succeeded in their ecological niche through close coupling of their sensing and mechanical systems. Future integration of electrosense and ribbon fin technology into a knifefish robot should likewise result in a vehicle capable of navigating complex 3D geometries unreachable with current underwater vehicles, as well as provide insights into how to design mobile robots that integrate high bandwidth sensing with highly responsive multidirectional movement.

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This paper uses two symmetrical models, the passive compass-gait biped and a five-link 3-D biped, to computationally investigate the cause and function of gait asymmetry. We show that for a range of slope angles during passive 2-D walking and mass distributions during controlled 3-D walking, these models have asymmetric walking patterns between the left and right legs due to the phenomenon of spontaneous symmetry-breaking. In both cases a stable asymmetric family of gaits emerges from a symmetric family of gaits as the total energy increases (e.g., fast speeds). The ground reaction forces of each leg reflect different roles, roughly corresponding to support, propulsion, and motion control as proposed by the hypothesis of functional asymmetry in able-bodied human walking. These results suggest that body mechanics, independent of neurophysiological mechanisms such as leg dominance, may contribute to able-bodied gait asymmetry.

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A major challenge in controlling multiple-input multiple output functional electrical stimulation systems is the large amount of time required to identify a workable system model due to the high dimensionality of the space of inputs. To address this challenge we are exploring optimal methods to sample the input space. In this paper we present two methods for optimally sampling isometric muscle force recruitment curves. One method maximizes the information about the recruitment curve parameters, and the second method minimizes the average variance of the predicted output force. We compared these methods to two previously-used methods in simulation. The simulation model was identified from recruitment data collected during experiments with a human subject with a high spinal cord injury. The optimal sampling methods on average produced estimates of the output force with less error than the two previously-used methods. The optimal sampling methods require fewer system identification experiments to identify models with similar output prediction accuracy.

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This paper computationally investigates whether gait asymmetries can be attributed in part to basic bipedal mechanics independent of motor control. Using a symmetrical rigid-body model known as the compass-gait biped, we show that changes in environmental or physiological parameters can facilitate asymmetry in gait kinetics at fast walking speeds. In the environmental case, the asymmetric family of high-speed gaits is in fact more stable than the symmetric family of low-speed gaits. These simulations suggest that lower extremity mechanics might play a direct role in functional and pathological asymmetries reported in human walking, where velocity may be a common variable in the emergence and growth of asymmetry.

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This paper uses a symmetrical five-link 3D biped model to computationally investigate the cause, function, and benefit of gait asymmetry. We show that for a range of mass distributions, this model has asymmetric walking patterns between the left and right legs, which is due to a phenomenon known as period-doubling bifurcation. The ground reaction forces of each leg reflect different roles, roughly corresponding to support, propulsion, and motion control as proposed by the hypothesis of functional asymmetry in human walking. These results suggest that natural mechanics could be responsible for asymmetry in able-bodied walking, rather than neurophysiological mechanisms such as leg dominance.

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This paper is focused on investigating force regulation strategies employed by human central nervous system (CNS). The mechanism responsible for force control is extremely important in people's lives, but not yet well understood. We formulate the general model of force regulation and identify several possible control strategies. An experimental approach is used to determine which of the force control strategies could actually be used by the CNS. Obtained results suggest that the force regulation process involves not only the pure force controller, but also a coupled motion controller, relying on the internal model of the environment.

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To manipulate an object, we must simultaneously control the contact forces exerted on the object and the movements of our hand. Two alternative views for manipulation have been proposed: one in which motions and contact forces are represented and controlled by separate neural processes, and one in which motions and forces are controlled jointly, by a single process. To evaluate these alternatives, we designed three tasks in which subjects maintained a specified contact force while their hand was moved by a robotic manipulandum. The prescribed contact force and hand motions were selected in each task to induce the subject to attain one of three goals: (1) exerting a regulated contact force, (2) tracking the motion of the manipulandum, and (3) attaining both force and motion goals concurrently. By comparing subjects' performances in these three tasks, we found that behavior was captured by the summed actions of two independent control systems: one applying the desired force, and the other guiding the hand along the predicted path of the manipulandum. Furthermore, the application of transcranial magnetic stimulation impulses to the posterior parietal cortex selectively disrupted the control of motion but did not affect the regulation of static contact force. Together, these findings are consistent with the view that manipulation of objects is performed by independent brain control of hand motions and interaction forces.

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The ability to discriminate an object's shape and mechanical properties from touch is one of the most fundamental somatosensory functions. When exploring physical properties of an object, such as stiffness and curvature, humans probe the object's surface and obtain information from the many sensory receptors in their upper limbs. This sensory information is critical for the guidance of actions. We studied how humans acquire an internal representation of the shape and mechanical properties of surfaces and how this information affects the execution of trajectories over the surface. Experiments involved subjects executing trajectories while holding a planar manipulandum that renders planar virtual objects with variable shape and mechanical properties. Subjects were instructed to make reaching movements with the hand between points on the boundary of a curved virtual disk of varying stiffness and curvature. The results suggest two classifications of adaptive responses: force perturbations and object boundaries. In the first case, a rectilinear hand movement is enforced by opposing the interaction forces. In the second case, the trajectory conforms to the object boundary so as to reduce interaction forces. While this dichotomy is evident for very rigid and very soft objects, the likelihood of an object boundary classification depended, in a smooth and monotonic way, on the average force experienced during the initial movements. Furthermore, the observed response across a variety of stiffness values lead to a constant average interaction force after adaptation. This suggests that the nervous system may select from the two responses through a mechanism that attempts to establish a constant interaction force.

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Smooth, frictionless, kinematic constraints on the motion of a grasped object reduce the motion freedoms at the hand, but add force freedoms, that is, force directions that do not affect the motion of the object. We are studying how subjects make use of these force freedoms in static and dynamic manipulation tasks. In this study, subjects were asked to use their right hand to hold stationary a manipulandum being pulled with constant force along a low-friction linear rail. To accomplish this task, subjects had to apply an equal and opposite force along the rail, but subjects were free to apply a force against the constraint, orthogonal to the pulling force. Although constraint forces increase the magnitude of the total force vector at the hand and have no effect on the task, we found that subjects applied significant constraint forces in a consistent manner dependent on the arm and constraint configurations. We show that these results can be interpreted in terms of an objective function describing how subjects choose a particular hand force from an infinite set of hand forces that accomplish the task. Without assuming any particular form for the objective function, the data show that its level sets are convex and scale invariant (i.e., the level set shapes are independent of the hand-force magnitude). We derive the level sets, or "isocost" contours, of subjects' objective functions directly from the experimental data.

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