Publications

Peer-Reviewed Journal Papers


  • Virtual Constraint Control of a Powered Prosthetic Leg: From Simulation to Experiments with Transfemoral Amputees
    R. Gregg T. Lenzi, L. Hargrove, and J. Sensinger. IEEE Transactions on Robotics, 2014, accepted for publication. (Draft available upon request)

    Abstract: Recent powered (or robotic) prosthetic legs independently control different joints and time periods of the gait cycle, resulting in control parameters and switching rules that can be difficult to tune by clinicians. This challenge might be addressed by a unifying control model used by recent bipedal robots, in which virtual constraints define joint patterns as functions of a monotonic variable that continuously represents the gait cycle phase. In the first application of virtual constraints to amputee locomotion, this paper derives exact and approximate control laws for a partial feedback linearization to enforce virtual constraints on a prosthetic leg. We then encode a human-inspired invariance property called effective shape into virtual constraints for the stance period. After simulating the robustness of the partial feedback linearization to clinically meaningful conditions, we experimentally implement this control strategy on a powered transfemoral leg. We report the results of three amputee subjects walking overground and at variable cadences on a treadmill, demonstrating the clinical viability of this novel control approach.

  • Evidence for a Time-Invariant Phase Variable in Human Ankle Control
    R. Gregg, E. Rouse, L. Hargrove, and J. Sensinger. PLoS ONE 9(2):e89163, 2014, doi:10.1371/journal.pone.0089163. (Full Text Open Access)

    Abstract: Human locomotion is a rhythmic task in which patterns of muscle activity are modulated by state-dependent feedback to accommodate perturbations. Two popular theories have been proposed for the underlying embodiment of phase in the human pattern generator: a time-dependent internal representation or a time-invariant feedback representation (i.e., reflex mechanisms). In either case the neuromuscular system must update or represent the phase of locomotor patterns based on the system state, which can include measurements of hundreds of variables. However, a much simpler representation of phase has emerged in recent designs for legged robots, which control joint patterns as functions of a single monotonic mechanical variable, termed a phase variable. We propose that human joint patterns may similarly depend on a physical phase variable, specifically the heel-to-toe movement of the Center of Pressure under the foot. We found that when the ankle is unexpectedly rotated to a position it would have encountered later in the step, the Center of Pressure also shifts forward to the corresponding later position, and the remaining portion of the gait pattern ensues. This phase shift suggests that the progression of the stance ankle is controlled by a biomechanical phase variable, motivating future investigations of phase variables in human locomotor control.

Peer-Reviewed Conference Proceedings


  • Experimental Effective Shape Control of a Powered Transfemoral Prosthesis
    R. Gregg, T. Lenzi, N. Fey, L. Hargrove, and J. Sensinger. In IEEE International Conference on Rehabilitation Robotics, Seattle, WA, 2013.
    (PDF, Experiment Movie)

    Abstract: This paper presents the design and experimental implementation of a novel feedback control strategy that regulates effective shape on a powered transfemoral prosthesis. The human effective shape is the effective geometry to which the biological leg conforms--through movement of ground reaction forces and leg joints--during the stance period of gait. Able-bodied humans regulate effective shapes to be invariant across conditions such as heel height, walking speed, and body weight, so this measure has proven to be a very useful tool for the alignment and design of passive prostheses. However, leg joints must be actively controlled to assume different effective shapes that are unique to tasks such as standing, walking, and stair climbing. Using our previous simulation studies as a starting point, we model and control the effective shape as a virtual kinematic constraint on the powered Vanderbilt prosthetic leg with a custom instrumented foot. An able-bodied subject used a by-pass adapter to walk on the controlled leg over ground and over a treadmill. These preliminary experiments demonstrate, for the first time, that effective shape (or virtual constraints in general) can be used to control a powered prosthetic leg.

  • Biomimetic Virtual Constraint Control of a Transfemoral Powered Prosthetic Leg
    R. Gregg and J. Sensinger. In American Control Conference, Washington, DC, 2013. (PDF, Simulation Movie)

    Abstract: This paper presents a novel control strategy for a powered knee-ankle prosthesis based on biomimetic virtual constraints. We begin by deriving kinematic constraints for the "effective shape" of the human leg during locomotion. This shape characterizes ankle and knee motion as a function of the Center of Pressure (COP)--the point on the foot sole where the ground reaction force is imparted. Since the COP moves monotonically from heel to toe during steady walking, we adopt the COP as the phase variable of an autonomous feedback controller. We show that our kinematic constraints can be enforced virtually by an output linearizing controller that uses only feedback available to sensors onboard a prosthetic leg. This controller produces walking gaits with human-like knee flexion in simulations of a 6-link biped with feet. Hence, both knee and ankle control can be coordinated by one simple control objective: maintaining a constant-curvature effective shape.

  • Simultaneous Control of the Compass-Gait Biped for Maintaining Symmetric Gait Across All Mass Ratios
    A. Nanjangud and R. Gregg. In American Control Conference, Portland, OR, 2014.

    Abstract: It is known that the hybrid dynamical model of a compass-gait biped, which is used here to represent a patient using ankle-foot prostheses on both legs, exhibits a loss of stable period-one symmetric gait with increasing hip-to-leg mass ratio. For higher mass ratios, the period-one gait becomes unstable and bifurcates into a period-two asymmetric gait. In this work, the continuous-time single-support phase of the compass-gait biped is linearized about the upright position and simultaneously stabilized by a linear time-invariant controller that is simple, single- input single-output, and only second-order. This controller, when simulated with the underactuated non- linear hybrid compass-gait biped model, is shown to maintain stable period-one symmetric gait across all physiologically meaningful mass distributions of the compass-gait biped.

  • A Survey of Phase Variable Candidates of Human Locomotion
    D. Villarreal and R. Gregg. In IEEE Engineering in Medicine and Biology Conference, Chicago, IL, 2014. (PDF)

    Abstract: Studies show that the human nervous system is able to parameterize gait cycle phase using sensory feedback. In the field of bipedal robots, the concept of a phase variable has been successfully used to mimic this behavior by parameterizing the gait cycle in a time-independent manner. This approach has been applied to control a powered transfemoral prosthetic leg, but the proposed phase variable was limited to the stance period of the prosthesis only. In order to achieve a more robust controller, we attempt to find a new phase variable that fully parameterizes the gait cycle of a prosthetic leg. The angle with respect to a global reference frame at the hip is able to monotonically parameterize both the stance and swing periods of the gait cycle. This survey looks at multiple phase variable candidates involving the hip angle with respect to a global reference frame across multiple tasks including level-ground walking, running, and stair negotiation. In particular, we propose a novel phase variable candidate that monotonically parameterizes the whole gait cycle across all tasks, and does so particularly well across level-ground walking. In addition to furthering the design of robust robotic prosthetic leg controllers, this survey could help neuroscientists and physicians study human locomotion across tasks from a time-independent perspective.

  • Simultaneous Control of Virtual Constraints for Ankle-Foot Prostheses
    A. Nanjangud and R. Gregg. To appear in Invited Session on Physical Human-Robot Interactions, ASME Dynamic Systems & Control Conf., San Antonio, TX, 2014. (PDF)

    Abstract: Amputee locomotion can benefit from recent advances in robotic prostheses, but their control systems design poses challenges. Prosthesis control typically discretizes the nonlinear gait cycle into phases, with each phase controlled by different linear controllers. Unfortunately, real-time identification of gait phases and tuning of controller parameters limit implementation. Recently, biped robots have used phase variables and virtual constraints to characterize the gait cycle as a whole. Although phase variables and virtual constraints could solve issues with discretizing the gait cycle, the virtual constraints method from robotics does not readily translate to prosthetics because of hard-to-measure quantities, like the interaction forces between the user and prosthesis socket, and prosthesis parameters which are often altered by a clinician even for a known patient. We use the simultaneous stabilization approach to design a low-order, linear time-invariant controller for ankle prostheses independent of such quantities to enforce a virtual constraint. We show in simulation that this controller produces suitable walking gaits for a simplified amputee model.

  • Hybrid Invariance and Stability of a Feedback Linearizing Controller for Powered Prostheses
    A. Martin and R. Gregg. Submitted to American Control Conf., Chicago, IL, 2015.

    Abstract: The development of powered lower-limb prostheses has the potential to significantly improve amputees' quality of life. Currently, the control schemes for most powered prostheses are impedance-based and rely on the amputee to fully coordinate the motion and stabilize the gait. By utilizing hybrid zero dynamics (HZD)-based control, more intelligent prostheses could be developed. Originally developed to control bipedal robots, HZD-based control specifies the motion of the actuated degrees of freedom using output functions to be zeroed and the required torques are calculated using feedback linearization. Previous work showed that an HZD-like prosthesis controller can successfully control the stance phase of gait. This paper shows that an HZD-based prosthesis controller can be used for the entire gait cycle, and further, that feedback linearization can be performed using only information measured with onboard sensors. Conditions to insure hybrid invariance and an analytic metric for orbital stability of a two-step periodic gait are also developed.

Conference Presentations


  • The Hypothesis of Feedback Pattern Generation in Human Locomotion
    R. Gregg, E. Rouse, L. Hargrove, and J. Sensinger. In Dynamic Walking Conference, Pittsburgh, PA, June 2013. (Abstract PDF, Talk Video)

Visit the PI's personal publication page for past publications.