Task-agnostic controllers for partial-assist lower-limb exoskeletons aim to reliably mimic biological torque while seamlessly adapting to changing movement patterns. However, current approaches relying on hidden state estimators or neural networks lack explainability and safety guarantees, while force amplification methods risk instability with an inherent trade-off between sensitivity and robustness to control inputs. Energy shaping control uses a kinematic model-based framework to provide predictable, stable assistance, though its traditional passive form limits biomimetic performance. Previous work relaxed the strict passivity requirements to improve biomimicry but reduced the stability guarantees. This paper presents an optimization-based extension of the energy-shaping control framework that combines the stability benefits of energy shaping with the intuitive biomimicry of force amplification. Our framework enables controlled trade-offs between sensitivity to changing human impedance and high performance through adjustable cost contributions of force amplification and model-based terms. We provide theoretical guarantees of closed-loop stability to an invariant set under human joint impedance control, supported by empirical validation of stability characteristics of an ankle exoskeleton under varying controller passivity constraints. A study of ten able-bodied participants using bilateral ankle exoskeletons demonstrates that the biomimetic controller reduced biological ankle torque by 19.1% across various activities of daily life.

Exoskeleton controllers have recently employed machine learning (ML) techniques to provide appropriate assistance throughout the terrains of the real world. One successful approach has been to learn a mapping between an exoskeleton wearer's kinematic measurements and a gait state vector that encodes how the wearer is currently walking (i.e. gait phase, speed), and then dynamically update the assistance based on the gait state. However, these methods require paired datasets of input kinematics to output gait states, which usually involves manual, time-consuming labeling of data from participants wearing specific exoskeletons and thus limits the scalability of these ML methods. A prior solution to this challenge—leveraging large pre-labeled datasets of normative human walking—introduces another problem, in that networks trained on these datasets learn only normative locomotion patterns, and thus may deteriorate when the data are changed by wearing the exoskeleton itself. In this context, we present an unsupervised-learning-based approach to both bypass the requirement of labeled data for gait state prediction and address the difficulty of domain adaptation from normative to exoskeleton-assisted walking. We validate our method in a set of walking simulations that featured exoskeleton data from 14 participants. This model showed significant improvements in state estimation relative to a model trained solely on pre-labeled normative walking, while also not requiring ground truth labels. This work presents a foundation that demonstrates labeled, device-specific data may not be required for predicting walking behavior in real time.

Springs are essential mechanical elements that are used across a wide variety of industries and mechanisms. Common across many spring types and applications is the importance of compactness, low mass and customizability. In this paper, we present a novel rotary spring design that is lightweight, compact and customizable. In addition, we empirically validate the design by experimentally quantifying the performance of two test springs on a custom dynamometry testbed. Our two-part spring geometry is comprised of a central rotating gear-like cam shaft, and a disk that includes a circular array of radially-spaced tapered cantilevered beams. The two springs that we designed and tested matched desired performance specifications within 3–6%, confirming the efficacy of this unique design approach.

Emerging partial-assistance exoskeletons can enhance able-bodied performance and aid people with patho-logical gait or age-related immobility. However, every person walks differently, which makes it difficult to directly compute assistance torques from joint kinematics. Gait-state estimation-based controllers use phase (normalized stride time) and task variables (e.g., stride length and ground inclination) to parameterize the joint torques. Using kinematic models that depend on the gait-state, prior work has used an Extended Kalman filter (EKF) to estimate the gait-state online. However, this EKF suffered from kinematic errors since it used a subject-independent measurement model, and it is still unknown how personalization of this measurement model would reduce gait-state tracking error. This paper quantifies how much gait-state tracking improvement a personalized measurement model can have over a subject-independent measurement model when using an EKF-based gait-state estimator. Since the EKF performance depends on the measurement model covariance matrix, we tested on multiple different tuning parameters. Across reasonable values of tuning parameters that resulted in good performance, personalization improved estimation error on average by 8.5 ± 13.8% for phase (mean ± standard deviation), 27.2$\pm \ 8.1{\%}$for stride length, and 10.5$\pm \ 13.5{\%}$for ground inclination. These findings support the hypothesis that personalization of the measurement model significantly improves gait-state estimation performance in EKF based gait-state tracking$(P \ll 0.05)$, which could ultimately enable reliable responses to faster human gait changes.

Modern exoskeletons are typically developed to optimize for a single, physiological objective, the “gold standard” of which is a reduction of the wearer's metabolic rate. However, recent research suggests that these changes in metabolic rate are not yet perceivable on average. To address this gap, this study explores a novel economic value metric to quantify the value of exoskeleton assistance. The overarching goal of this work is the development of a perceptible metric that leverages the user experience to quantify exoskeleton success. We use the Vickrey second-price auction to obtain the monetary compensation needed for participants to continue walking for consecutive two-minute bouts. Comparing the participant's bidding trends when wearing and not wearing an exoskeleton captures the economic value of the experience, termed Marginal Value (MV). To reduce the logistical burden of the auction, we simulated human participants (robo-bidders) to compete alongside real participants. This work presents a sensitivity analysis to understand how the number and bidding behavior of the robo-bidders affects our economic value metric, MV. We found that MV was not significantly affected by the number of robo-bidders or their bidding behavior (i.e. effort rate). The bidding behavior of the human participants was affected by the robo-bidder effort rate, indicating that there is interplay in the bidding dynamics among the auction participants, but these changes do not significantly affect the marginal value. This study tentatively validates the current approach in generating our proposed metric for exoskeleton success, paving the way for economic value to be further explored as a holistic, personalized metric for the development of lower-limb exoskeletons.

Robotic ankle exoskeletons have been shown to reduce human effort during walking. However, existing ankle exoskeleton control approaches are limited in their ability to apply biomimetic torque across diverse tasks outside of the controlled lab environment. Energy shaping control can provide task-invariant assistance without estimating the user's state, classifying task, or reproducing pre-defined torque trajectories. In previous work, we showed that an optimally task-invariant energy shaping controller implemented on a knee-ankle exoskeleton reduced the effort of certain muscles for a range of tasks. In this paper, we extend this approach to the sensor suite available at the ankle and present its implementation on a commercially-available, bilateral ankle exoskeleton. An experiment with three healthy subjects walking on a circuit and on a treadmill showed that the controller can approximate biomimetic profiles for varying terrains and task transitions without classifying tasks or switching control modes.

Positive biomechanical outcomes have been reported with lower-limb exoskeletons in laboratory settings, but these devices have difficulty delivering appropriate assistance in synchrony with human gait as the task or rate of phase progression change in real-world environments. This paper presents a controller for an ankle exoskeleton that uses a data-driven kinematic model to continuously estimate the phase, phase rate, stride length, and ground incline states during locomotion, which enables the real-time adaptation of torque assistance to match human torques observed in a multi-activity database of 10 able-bodied subjects. We demonstrate in live experiments with a new cohort of 10 able-bodied participants that the controller yields phase estimates comparable to the state of the art, while also estimating task variables with similar accuracy to recent machine learning approaches. The implemented controller successfully adapts its assistance in response to changing phase and task variables, both during controlled treadmill trials (N=10, phase RMSE: 4.8 ± 2.4%) and a real-world stress test with extremely uneven terrain (N=1, phase RMSE: 4.8 ± 2.7%).

Natural dynamics, nonlinear optimization, and, more recently, convex optimization are available methods for stiffness design of energy-efficient series elastic actuators. Natural dynamics and general nonlinear optimization only work for a limited set of load kinetics and kinematics, cannot guarantee convergence to a global optimum, or depend on initial conditions to the numerical solver. Convex programs alleviate these limitations and allow a global solution in polynomial time, which is useful when the space of optimization variables grows (e.g., when designing optimal nonlinear springs or co-designing spring, controller, and reference trajectories). Our previous work introduced the stiffness design of series elastic actuators via convex optimization when the transmission dynamics are negligible, which is an assumption that applies mostly in theory or when the actuator uses a direct or quasi-direct drive. In this work, we extend our analysis to include friction at the transmission. Coulomb friction at the transmission results in a non-convex expression for the energy dissipated as heat, but we illustrate a convex approximation for stiffness design. We experimentally validated our framework using a series elastic actuator with specifications similar to the knee joint of the Open Source Leg, an open-source robotic knee-ankle prosthesis.

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 resonance as stiffness and inertia vary. We validate this concept with an elbow-joint exoskeleton testbed (attached to a subject) by experimentally varying joint stiffness behavior, exoskeleton inertia, and the strength augmentation gain. 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 (via a statistical F-test). Moreover, this term contributes more to model accuracy than the 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 down to 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.

The mechanical design of robotic hands has been converging towards low-inertia, tendon-driven strategies. As tendon driven robotic fingers are serial chain systems, routing strategies with compliant tendons lead to multi-articular coupling between the degrees of freedom. We propose a generalized analysis of such serial chain linkages with coupled passive joint stiffnesses. We analyze the effect of such coupling on maximum achievable stiffness control boundaries while maintaining passivity at the actuators by analytically deriving the boundaries. We believe that we can use this information to form mechanical design guidelines for intelligently selecting arrangements of compliance elements (mechanical springs) and transmission strategies, i.e. tendon routing and pulley radii, to provide intrinsic stability and customizable controller stiffness limits for high performance manipulation in robotic hands.

This paper considers the problem of numerically efficient planning for legged robot locomotion, aiming towards reactive multi-contact planning as a reliability feature. We propose to decompose the problem into two parts: an extremely low dimensional kinematic search, which only adjusts a geometric path through space; and a dynamic optimization, which we focus on in this paper. This dynamic optimization also includes the selection of foot steps and hand-holds-in the special case of instantaneous foot re-location. This case is interesting because (1) it is a limiting behavior for algorithms with a foot switching cost, (2) it may have merit as a heuristic to guide search, and (3) it could act as a building block towards algorithms which do consider foot transition cost. The algorithm bears similarity both to phase space locomotion planning techniques for bipedal walking and the minimum time trajectory scaling problem for robot arms. A fundamental aspect of the algorithm's efficiency is its use of linear programming with reuse of the active set of inequality constraints. Simulation results in a simplified setting are used to demonstrate the planning of agile locomotion behaviors.

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.

Legged robots naturally exhibit continuous and discrete dynamics when maneuvering over level-ground and uneven terrains. In recent years, numerous studies have focused on locomotion hybrid dynamics. However, locomotion on more challenging terrains such as split wedges in Figure 1 has rarely been explored, let alone its hybrid dynamics. In this study, we specifically focus on a two-phase hybrid automaton formulation for this highly steep wedge locomotion. This automaton incorporates both multi-contact and flight single contact phase motions. To dynamically balance and jump upwards on this wedge, an aperiodic phase space planning is used for trajectory generations. Three control strategies are employed simultaneously: internal force control, linear and angular momentum control. Finally, simulation results are shown to verify our strategy's effectiveness.

This paper presents a control scheme for ensuring that a 3D, under-actuated, point-foot biped robot remains balanced while walking. It achieves this by observing the center of mass (COM) position error relative to a reference path and re-planning a new reference trajectory to remove this error at every step. The Prismatic Inverted Pendulum Model (PIPM) is used to simplify behavioral analysis of the robot. We use phase space techniques to plan the COM trajectories and foot placement. While obtaining a stable path using this simplified model is easy, when applied to a real robot, there will usually be deviation from the expected path due to modeling inaccuracies. Although fully-actuated robots can reduce the deviation with relatively simple feedback control loops, when working with under-actuated robots, it is challenging to design such a feedback control loop. Our approach is based on continuous re-planning. By planning the path of the next step based on the observed initial error, we can find the proper landing location of each step. For each step we allocate sufficient time to avoid disturbances from the moment induced by the moving leg, which is not modeled in the PIPM. Our control scheme relies on the PIPM instead of the Linear Inverted Pendulum Model (LIPM) to enable non-planar COM motion, which is essential for rough terrain locomotion. We show simulation results that include full multi-body dynamics, friction, and ground reaction forces.

In order to make unintentional physical interaction with robots safer for humans, we consider compliant control of an omnidirectional wheeled base. In this paper we present a fully holonomic mobile robot system which achieves compliant motion via force control, improving over previous pseudo-omnidirectional mobile systems by being fully omnidirectional. We explain our robot's drive train, and present an experimental validation of our actuator control strategy. Using a smith predictor and a simple delay-based plant model, we demonstrate compliance and safe interaction in both the mobile system alone and as the base of a wheeled mobile manipulator style system.