Peer-Reviewed Journal Papers

  • A Robust Parameterization of Human Gait Patterns Across Phase-Shifting Perturbations. D. Villarreal, H. Poonawala, and R. Gregg. IEEE Transactions on Robotics, 2015, under review. (Experiment Movie)

    Abstract: The phase of human gait is difficult to quantify accurately in the presence of disturbances. In contrast, bipedal robots use time-independent controllers relying on a mechanical phase variable to synchronize joint patterns through the gait cycle. This concept has inspired studies to determine if human joint patterns can also be represented by a mechanical variable. Although many phase variable candidates have been proposed, it remains unclear which, if any, provide a robust representation of phase for gait analysis or control. In this paper we analytically derive an ideal phase variable (the hip phase angle) that is provably monotonic and bounded throughout the gait cycle. To examine the robustness of this phase variable, ten able-bodied human subjects walked over a perturbation platform that randomly applied phase-shifting perturbations to the stance leg. A statistical analysis found the correlations between nominal and perturbed joint trajectories to be significantly greater when parameterized by the hip phase angle (0.95+) than by time or horizontal hip position. The phase angle parameterization also minimized deviation from the nominal periodic orbit in a manner indicative of orbital stability. Finally, an analysis of interlimb coordination found an ipsilateral phase parameterization to be more robust than a contralateral phase parameterization.

  • Incorporating Human-like Walking Variability in an HZD-Based Bipedal Model. A. Martin and R. Gregg. IEEE Transactions on Robotics, 2015, under review.

    Abstract: Predictive simulations of human walking could be used to investigate a wide range of scientific questions, such as the effect of exoskeletons and prostheses. Promising moderately complex models of human walking have been developed using the robotics control technique hybrid zero dynamics (HZD). Fall risk is of great interest to clinicians and can be quantified using gait variability. Unfortunately, existing simulations of human walking only consider the mean motion, so they cannot be used to investigate fall risk. This work determines how to incorporate human-like variability into an HZD-based healthy human model to generate a more realistic gait. To do so, the output function used for feedback linearization is augmented with a sinusoidal variability function and a polynomial correction function. The variability function captures the variation in joint angles and is based on recent work with experimental data. The correction function is used to prevent the variability function from growing uncontrollably. The necessity of the correction function and the improvements with a reduction of stance ankle variability are demonstrated with simulation results. The variability in the temporal parameters is also shown to be similar to the corresponding experimental values.

  • Underactuated Potential Energy Shaping with Contact Constraints: Application to a Powered Knee-Ankle Orthosis. G. Lv and R. Gregg. IEEE Transactions on Control Systems Technology, 2015, under review.

  • Characterizing and Modeling the Joint-level Variability in Human Walking. A. Martin, D. Villarreal, and R. Gregg. Gait & Posture, 2015, under review.

    Abstract: Although human gait is often assumed to be periodic, signicant variability exists. This variability appears to provide different information than the underlying periodic signal, particularly about fall risk. Most studies on variability have either used step-to-step metrics such as stride duration or point-wise standard deviations, neither of which explicitly capture the joint-level variability as a function of time. This work demonstrates that a second-order Fourier series for stance joints and a first-order Fourier series for swing joints can accurately capture the variability in joint angles as a function of time on a per-step basis for overground walking at the self-selected speed. It further demonstrates that a total of seven normal distributions, four linear relationships, and twelve continuity constraints can be used to describe how the Fourier series vary between steps. The ability of the proposed method to create curves that match human joint-level variability was evaluated both qualitatively and quantitatively using randomly generated curves.

  • Evaluation of Transradial Body-Powered Prostheses Using a Robotic Simulator. R. Ayub, D. Villarreal, R. Gregg, and F. Gao. Prosthetics & Orthotics International, 2015, under review.

    Abstract: Background: Transradial body powered prostheses are extensively used by upper limb amputees. This prosthesis requires large muscle forces and great concentration by the patient, often leading to discomfort, muscle fatigue, and skin breakdown, limiting the capacity of the amputee to conduct daily activities. Since body-powered prostheses are commonplace, understanding their optimal operation to mitigate these drawbacks would be clinically meaningful. Objectives: Find the optimal operation of the prosthesis where the activation force is minimized and the grip force is maximized. Study Design/Methods: A computer-controlled robotic amputee simulator capable of rapidly testing multiple elbow, shoulder, and scapular combinations of the residual human arm was constructed. It was fitted with a transradial prosthesis and used to systematically test multiple configurations. Results: We found that increased shoulder flexion, scapular abduction, elbow extension, and the placement of the ring harness near the vertebra C7 correlates with higher gripper operation efficiency, defined as the relation between grip force and cable tension. Conclusions: We conclude that force transmission efficiency is closely related to body posture configuration. These results could help guide practitioners in clinical practice as well as motivate future studies in optimizing the operation of a body-powered prosthesis.

  • 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, 30(6): 1455-1471, 2014, doi: 10.1109/TRO.2014.2361937.
    (PDF, Experiment Movie)

    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. (Open Access Text, Data)

    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

  • A Perturbation Mechanism for Investigations of Phase-Dependent Behavior in Human Locomotion. D. Villarreal, D. Quintero, and R. Gregg. Submitted to IEEE Int. Conf. Robotics & Biomimetics (ROBIO), Zhuhai, China, 2015.
  • Abstract: The concept of a phase variable, a mechanical measurement of the body's progression through the gait cycle, has been used to parameterize the leg joint patterns of autonomous bipedal robots, producing human-like gaits with robustness to external perturbations. It was recently proposed that the kinematic response of humans to a perturbation could also be parameterized by a phase variable. In order to properly study this phase variable hypothesis with human subjects, a custom perturbation mechanism was built to cause phase shifts in the gait cycle. The main goals of this study are to introduce the design of a novel perturbation mechanism and experimentally demonstrate its ability to effect phase changes during the gait cycle.

  • Orthotic Body-Weight Support Through Underactuated Potential Energy Shaping with Contact Constraints. G. Lv and R. Gregg. To appear in IEEE Conf. Decision & Control, Osaka, Japan, 2015.
  • Unifying the Gait Cycle in the Control of a Powered Prosthetic Leg. D. Quintero, A. Martin, and R. Gregg. In IEEE Int. Conf. Rehabilitation Robotics, Singapore, 2015. (PDF)

    Abstract: This paper presents a novel control strategy for an above-knee powered prosthetic leg that unifies the entire gait cycle, eliminating the need to switch between controllers during different periods of gait. Current control methods divide the gait cycle into several sequential periods each with independent controllers, resulting in many patient-specific control parameters and switching rules that must be tuned by clinicians. Having a single controller could reduce the number of control parameters to be tuned for each patient, thereby reducing the clinical time and effort involved in fitting a powered prosthesis for a lowerlimb amputee. Using the Discrete Fourier Transformation, a single virtual constraint is derived that exactly characterizes the desired actuated joint motion over the entire gait cycle. Because the output of the virtual constraint is defined as a periodic function of a monotonically increasing phase variable, no switching or resetting is necessary within or across gait cycles. The output function is zeroed using feedback linearization to produce a single, unified controller. The method is illustrated with simulations of a powered knee-ankle prosthesis in an amputee biped model and examples of systematically generated output functions for different walking speeds.

  • Hybrid Invariance and Stability of a Feedback Linearizing Controller for Powered Prostheses. A. Martin and R. Gregg. In American Control Conference, Chicago, IL, 2015. (PDF)

    Abstract: The development of powered lower-limb prostheses has the potential to significantly improve amputees' quality of life. By applying advanced control schemes, such as hybrid zero dynamics (HZD), to prostheses, more intelligent prostheses could be designed. 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 period of gait. This paper shows that an HZD-based prosthesis controller can be used for the entire gait cycle and that feedback linearization can be performed using only information measured with on-board sensors. An analytic metric for orbital stability of a twostep periodic gait is developed. The results are illustrated in simulation.

  • Simultaneous Control of Virtual Constraints for Ankle-Foot Prostheses. A. Nanjangud and R. Gregg. In Invited Session on Physical Human-Robot Interactions, ASME Dynamic Systems & Control Conference, San Antonio, TX, 2014.

    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.

  • 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.

  • 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.

  • 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.

Magazine Articles

  • Challenges for Control Research: Control of Powered Prosthetic Legs. R. Gregg, L. Hargrove, and J. Sensinger. The Impact of Control Technology, 2nd ed., T. Samad and A.M. Annaswamy (eds.), IEEE Control Systems Society, 2014, available at (PDF)

    Abstract: Amputee locomotion is slower, less stable, and requires more metabolic energy than able-bodied locomotion. Lower-limb amputees fall more frequently than able-bodied individuals and often struggle to navigate inclines such as ramps, hills, and especially stairs. These challenges can be attributed largely to the use of mechanically passive prosthetic legs, which do not contribute positively to the energetics of gait, as do the muscles of the biological leg. Powered (or robotic) prosthetic legs could significantly improve mobility and quality of life for lower-limb amputees (including nearly one million Americans), but control challenges limit the performance and clinical feasibility of today's devices

Conference Abstracts

  • Giving Up the Finite State Machine in the Control of Lower-Limb Wearable Robots?. D. Quintero, A. Martin, and R. Gregg. In Workshop on Rehabilitation Robotics and Human-Robot Interaction, IEEE Int Conf Robotics & Automation, Seattle, WA 2015. (PDF)

  • Determining the Sagittal Plane Function for a Model Prosthetic Foot. A. Martin, J. Smith, R. Gregg, and J. Schmiedeler. In American Society of Biomechanics, Columbus, OH, 2015.

  • Virtual Constraint Control of a Powered Prosthetic Leg: Experiments with Transfemoral Amputees. R. Gregg. In Dynamic Locomotion Workshop, Robotics: Science & Systems, Berkeley, CA, 2014. (PDF)

Recorded 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.