For robotic transtibial prosthesis control, the global tibia kinematics can be used to monitor gait cycle progression and command smooth and continuous actuation. In this work, these global tibia kinematics define a phase variable impedance controller (PVIC), which is implemented as the nonvolitional base controller within a hybrid volitional control framework (PVI-HVC). The gait progression estimation and biomechanic performance of one able-bodied individual walking on a robotic ankle prosthesis via a bypass adapter are compared for three control schemes: benchmark passive controller, PVIC, and PVI-HVC. The different actuation of each had a direct effect on the global tibia kinematics, but the average deviation between the estimated and ground truth gait percentages were 1.6%, 1.8%, and 2.1%, respectively, for each controller. Both PVIC and PVI-HVC produced good agreement with able-bodied kinematic and kinetic references. As designed, PVI-HVC results were similar to those of PVIC when the user used low volitional intent, but yielded higher peak plantarflexion, peak torque, and peak power when the user commanded high volitional input in late stance. This additional torque and power also allowed the user to volitionally and continuously achieve activities beyond level walking, such as ascending ramps, avoiding obstacles, standing on tip-toes, and tapping the foot. In this way, PVI-HVC offers the kinetic and kinematic performance of the PVIC during level ground walking, along with the freedom to volitionally pursue alternative activities.

Phase variable control based on global tibia kinematics holds promise for predicting gait cycle progression to continuously control robotic transtibial prostheses. Calibration of the phase variable is critical to ensure its monotonic behavior, to approach a linear relationship with gait percentage, and to accurately predict the percentage of gait. This paper compares four calibration approaches using data from 22 able-bodied subjects walking at 14 speeds [1]. The typical pure centering (PC) approach employed for thigh-based phase variables is not viable, yielding monotonic phase progression in fewer than half of the cases. An optimization (OPT) approach found monotonic calibrations in 305/308 cases with high linearity (average R2 of 0.91). Critical point centering (CPC) approximates the OPT performance, with 274/308 monotonic calibrations and an average R2 of 0.85, whereas the related vertical weighted average (VWA) approach was only slightly better than PC. All four approaches are similarly accurate in predicting gait percentage, staying within 5% at least 92.7% of the time.

This paper employs velocity decomposition of underactuated mechanical systems to determine the degree of dynamic coupling in the gaits of a two-link biped model. The degree of coupling between controlled and uncontrolled directions quantifies the control authority the system has over its unactuated degree of freedom. This paper shows that the amount of coupling is directly correlated to gait robustness, as seen through the size of the gait's region of attraction. The analytical measure of coupling is applied in the context of trajectory optimization to generate two-link gaits that maximize or minimize coupling. Simulation studies show that gaits maximizing coupling exhibit significantly superior robustness, as measured by 1) stochastic performance on uneven terrain, 2) ability to maintain desired walking speed under non-vanishing disturbances, 3) size of the region of attraction, and 4) robustness to model uncertainties.

This paper shows how CasADi’s state-of-the-art implementation of algorithmic differentiation can be leveraged to formulate and efficiently solve gait optimization problems, enabling rapid gait design for high-dimensional biped robots. Comparative studies on a 7-DOF planar biped show that CasADi generates optimal gaits 4 times faster than another existing advanced optimization package. The framework is also applied to simultaneously generate a gait and a feedback controller for 2 spatial bipeds: a 12-DOF model and a 20DOF model. Results suggest that CasADi’s unprecedented efficiency could provide a practical path toward real-time gait optimization for high-dimensional biped robots.

This paper introduces a new gait switching approach for underactuated biped walkers. The switching condition relies on a reduced region of attraction - that of the unactuated dynamics - which is shown to be sufficient to predict falls. A gait transition is accordingly stable (as in “the robot does not fall if the biped's state is within the reduced region of attraction of the switched-in gait when switching takes place. Two- and five-link biped models complete a sequence of random gait transitions using the switching logic. The condition is also used to enlarge the full region of stability of the five-link model by embedding feedback-stabilized trajectories from a gait library in a mapping. The mapping stitches stable trajectories to the orbit of the desired gait based on each gait's reduced region of attraction. This improves the robustness of the five-link model walking on uneven terrain without ground perception regardless of the size of the gait library.

This paper presents a study of the relationship between the magnitude of coupling between the actuated and unactuated degrees of freedom for an ankle-actuated biped robot and the robustness and cost of transport of the gait. It extends prior results that considered only the instantaneous coupling at individual poses to analyze the cumulative effects of coupling over entire trajectories. The coupling metric is general in that it can be computed directly from the Lagrangian of the system. By using a two-link biped model, a family of ankle-actuated candidate gaits defined by fourth-order Bézier polynomials is generated, and the feasibility of the gaits is verified in the sense that the unilateral constraint of ground reaction force is satisfied. The correlation between the coupling metric and the maximum magnitude of disturbance that can be rejected is significant. It indicates that robust gaits tend to have small coupling under zero disturbance so that the “reserve” coupling may be utilized to reject the disturbance. Moreover, gaits with smaller cost of transport under zero disturbances have smaller coupling and therefore should be more robust.

The reaction wheel stabilizer (RWS) concept for bipedal stabilization consists of a wheel that can be accelerated in order to impart a reaction torque on the rest of the biped. The beneficial effects of such a device (or emulation of such a device through limb motion) on transient body motions are not well understood. This work quantifies this phenomenon by comparing optimal trajectories for robots with and without an RWS in terms of energy efficiency and dynamic feasibility when attempting to execute speed transitions and disturbance response motions. Robots with RWS systems are able to more efficiently execute abrupt speed transitions, showing up to a 60% improvement in efficiency for single step transitions. In responding to forward push disturbances, the RWS improves efficiency by between 20 and 60% over the range of tested disturbances. These savings are significantly larger than those shown previously for periodic walking.

Reaction wheel systems (RWSs) are beneficial in improving bipedal walking stability, and theoretical work has shown that they can also improve the efficiency of preplanned walking motions. This work provides the first demonstration of RWS-related efficiency improvements on a physical robot and identifies the energy-saving paradigm. Gaits for a five-link planar biped are generated via trajectory optimization with and without reaction wheels. Comparisons of the resulting system behavior show a 5-10% efficiency advantage for robots with an RWS under typical walking conditions and a larger advantage near regions of marginal dynamic feasibility. The savings are mainly accomplished by enabling trajectories with better joint motor utilization, not by minimizing impact losses or acting as a kinetic energy recovery system. The RWS also improves centroidal angular momentum regulation, with the reduction in centroidal angular momentum amplitude reaching 30% at high speeds. Simulations and experiments with a five-link planar biped validate the efficiency improvements seen in optimization. This demonstrates the viability of using efficient inertial actuators to improve the efficiency of complex walking robots.

Inertial actuators, such as reaction wheels, have the potential to improve the stability and robustness of bipedal robots. While the stabilizing capabilities of reaction wheels follow naturally from physical laws, the effects on walking efficiency are less clear. This work examines those effects by comparing energy-optimal periodic gaits for a variety of under-actuated, five-link planar biped configurations. When energy consumption is normalized by total mass, bipeds equipped with reaction wheels have decreased walking cost compared to unequipped bipeds of the same mass across a wide range of conditions. At speeds equal to or higher than the optimal walking speed, reaction wheels can reduce walking cost by approximately 8%. When walking with large step lengths, reaction wheels decrease walking costs by more than 20% and allow bipeds to take longer steps. Efficiency improvements scale with the momentum capacity of the reaction wheel, but saturate for particularly large reaction wheels.

Robots walking under hybrid zero dynamics (HZD)-based control are susceptible to velocity disturbances because the controller is typically designed for one speed. LQR-based orbital stabilization control is one means to address this issue using feedback on the unactuated velocity. The approach, though, is difficult to implement in real time experimentally even on planar bipeds with relatively few links. This work extracts simple heuristics from simulated planar bipeds rejecting velocity disturbances under orbital stabilization control to approximate that functionality. The heuristics are layered on top of traditional HZD-based control of a five-link planar biped robot for experimental validation. Results show that the heuristically modified controller yields more efficient and more stable walking for the biped than does HZD-based control alone. It also enables rejection of larger decelerating disturbances and more rapid return to the desired walking cycle.

Current biped robots with articulated legs, even the most impressive to date, still lack the ability to execute dynamic motions such as jumping and running with comparable performance to biological systems. This work explores dynamic jumping with the planar biped prototype KURMET, which employs unidirectional series-elastic actuation at each of its joints. While this actuation scheme enables the performance of high-power dynamic movements like the jump, its presence complicates the jumping control problem and has prevented previous researchers from obtaining precise jump control in systems of reasonable complexity. To manage this problem, this paper develops a layered fuzzy control system for KURMET that realizes repeated dynamic hopping and accurate control of both torso height and velocity at each top of flight. An effective two-stage training approach is used for the fuzzy controller to learn the required, yet highly nonlinear, relationships between its inputs and outputs. Finally, the state machine employed at the lowest-level of control is used to achieve a maximal normalized jump height that outperforms most humans and can be sequenced with the hopping movement.

This paper presents a method of integrating kinematic mechanism design and hybrid system analysis for the design of a single-degree-of-freedom (DOF) planar biped robot that can achieve dynamic walking gaits that are stable. Reducing the DOF in a biped can result in a reduction of the complexity of the control strategies needed to enable stable walking. Although the biped designed by this procedure is restricted to a single gait, this biped may be less complex, lighter, and less costly to construct than one whose multiple DOF are coordinated via feedback.

The effect of asymmetrical body-mass distribution on the stability and dynamics of two-degree-of-freedom quadruped bounding in place is investigated in this study. An analytical stability criterion for bounding of quadrupeds with asymmetrical mass distribution is developed. Bounding is found to be passively stable in the Hamiltonian sense when the dimensionless pitch moment of inertia of the body is less than 1-/spl beta//sup 2/, where /spl beta/ is a dimensionless measure of the asymmetry. The criterion is derived under the assumptions of infinite leg stiffness and no energy loss. With energy dissipation modeled as linear damping in the legs, simulation results show that the criterion is independent of the value of leg stiffness and a conservative estimate of the critical inertia value. Body symmetry appears to be more favorable to stable bounding than asymmetry, but only slightly so in practicality. The results show that asymmetry offers some advantages when the dynamic characteristics of bounding are compared for symmetrical and asymmetrical models. Lower stride frequency, larger vertical displacement, and smaller duty factor are obtained with this more animal-like model.

An analytical stability criterion for bounding of quadrupeds with asymmetrical mass distribution is developed in this work. Bounding is found to be passively stable when the dimensionless pitch moment of inertia of the body is less than 1 - /spl beta//sup 1/, where /spl beta/ is a dimensionless measure of the asymmetry. The criterion is derived under the assumptions of infinite leg stiffness and no energy loss. Simulation results show that the criterion is independent of the value of leg stiffness and a conservative estimate of the critical inertia value when energy losses are modeled with linear damping. Body symmetry appears to be more favorable to stable bounding than asymmetry, but only slightly so in practicality.

Intelligent controllers are being used with increasing effectiveness on complex systems. This work verifies the effectiveness of fuzzy control, an intelligent method, on a single, articulated-leg that was designed to be used on a high-speed galloping quadruped. Intelligent methods are compared to other control methods in simulation and on the OSU DASH (Dynamic Articulated Structure for High-performance) leg. It is shown that the intelligent controllers outperform non-learning methods. Using fuzzy control, the OSU DASH leg performs stable hopping on a treadmill moving at 2.0 m/s.