James P. Schmiedeler

Intelligent control of quadruped gallops

In this paper, a new intelligent control approach for high-speed quadruped bounding and galloping gaits is presented. The controller is capable of learning the leg touchdown angles and leg thrusts required to track the desired running height and velocity of a quadruped in only one stride. Training of the controller is accomplished not with a mathematical model, but with simple rules based on a heuristic knowledge of the quadruped mechanics. The result is a controller that produces better velocity and height tracking characteristics than a Raibert-based controller and is robust to modeling errors. Additionally, by making use of the natural dynamics of the system, gait characteristics comparable to biological quadrupeds result. The status of a legged machine being constructed for demonstration of the control approach and further study of the characteristics of galloping is also presented.

Design and control of a planar bipedal robot ERNIE with parallel knee compliance

This paper presents the development of the planar bipedal robot ERNIE as well as numerical and experimental studies of the influence of parallel knee joint compliance on the energetic efficiency of walking in ERNIE. ERNIE has 5 links—a torso, two femurs and two tibias—and is configured to walk on a treadmill so that it can walk indefinitely in a confined space. Springs can be attached across the knee joints in parallel with the knee actuators. The hybrid zero dynamics framework serves as the basis for control of ERNIE’s walking. In the investigation of the effects of compliance on the energetic efficiency of walking, four cases were studied: one without springs and three with springs of different stiffnesses and preloads. It was found that for low-speed walking, the addition of soft springs may be used to increase energetic efficiency, while stiffer springs decrease the energetic efficiency. For high-speed walking, the addition of either soft or stiff springs increases the energetic efficiency of walking, while stiffer springs improve the energetic efficiency more than do softer springs.

Design and experimental implementation of a hybrid zero dynamics-based controller for planar bipeds with curved feet

This paper extends the use of virtual constraints and hybrid zero dynamics (HZD), a successful control strategy for point-foot bipeds, to the design of controllers for planar curved foot bipeds. Although the rolling contact constraint at the foot–ground interface increases complexity somewhat, the measure of local stability remains a function of configuration only, and a closed-form solution still determines the existence of a periodic orbit. The formulation is validated in experiment using the planar five-link biped ERNIE. While gaits designed for point feet yielded stable walking when ERNIE was equipped with curved feet, errors in both desired speed and joint tracking were significantly larger than for gaits designed for the correct radius curved feet. Thus, HZD-based control of this biped is shown to be robust to some modeling error in the foot radius, but at the same time, to require consideration of foot radius to achieve predictably reliable walking gaits. Additionally, under HZD-based control, this biped walked with lower specific energetic cost of transport and joint tracking errors for matched curved foot gait design and hardware compared to matched point-foot gait design and hardware.

Enhanced feedback in balance rehabilitation using the Nintendo Wii Balance Board

Balance retraining is a critical part of rehabilitation for many individuals following neuro-trauma such as stroke. The WeHab system described in this paper is a low-cost rehabilitation instrument suite centered around the Nintendo Wii Balance Board that has the potential to enhance rehabilitation for patients with balance disorders. Using the WeHab system, therapists can lead patients through normal rehabilitation exercises with the added benefit of visual biofeedback based on center of pressure location. Patient improvement can be tracked by the WeHab system through objective analysis of trends both within a single session and from one session to the next. Pilot data from several patients receiving inpatient therapy using the WeHab system at the Wound Care center at Memorial Hospital in South Bend, IN, indicate the potential benefit that the system could bring to balance rehabilitation. Specifically, the details of and results from sit-to-stand, weight-shifting, and stepping activities are presented for pilot subjects. Further expansion of the WeHab system is planned, including incorporation of auditory feedback. Future work also includes more structured studies of the effects of the WeHab system on balance recovery.

A framework for the control of stable aperiodic walking in underactuated planar bipeds

This paper presents a new definition of stable walking for point-footed planar bipedal robots that is not necessarily periodic. The inspiration for the definition is the commonly-held notion of stable walking: the biped does not fall. Somewhat more formally, biped walking is shown to be stable if the trajectory of each step places the robot in a state at the end of the step for which a controller is known to exist that generates a trajectory for the next step with this same property. To make the definition useful, an algorithm is given to verify if a given controller induces stable walking in the given sense. Also given is a framework to synthesize controllers that induce stable walking. The results are illustrated on a 5-link biped ERNIE in simulation and experiment.

The Mechanics of Quadrupedal Galloping and the Future of Legged Vehicles

Previous studies have noted that biological quadrupeds adjust their gaits when encountering drag in their locomotion. This paper investigates the hypothesis that these gait adjustments allow the legs to operate at an optimal working length when generating thrust. A 5-DoF dynamic model of a quadruped having a rigid trunk and massless legs is formulated. This model reflects the dimensions and inertial properties of a galloping machine the authors are designing. The constrained, steady-state motion equations governing the transverse and rotary gallops of the model are solved numerically for various levels of drag. The footfall phasing solutions for both forms of the gallop approach a partially in-phase gait, the half-bound, as drag increases. These gait transitions are the result of constraints requiring the legs to operate at their optimal working length when in contact with the terrain. Thus, the behavior of the model supports the original hypothesis. This paper also includes a discussion of future research directions in the field of artificial legged locomotion.

Predicting human walking gaits with a simple planar model

Models of human walking with moderate complexity have the potential to accurately capture both joint kinematics and whole body energetics, thereby offering more simultaneous information than very simple models and less computational cost than very complex models. This work examines four- and six-link planar biped models with knees and rigid circular feet. The two differ in that the six-link model includes ankle joints. Stable periodic walking gaits are generated for both models using a hybrid zero dynamics-based control approach. To establish a baseline of how well the models can approximate normal human walking, gaits were optimized to match experimental human walking data, ranging in speed from very slow to very fast. The six-link model well matched the experimental step length, speed, and mean absolute power, while the four-link model did not, indicating that ankle work is a critical element in human walking models of this type. Beyond simply matching human data, the six-link model can be used in an optimization framework to predict normal human walking using a torque-squared objective function. The model well predicted experimental step length, joint motions, and mean absolute power over the full range of speeds.

A Unidirectional Series-Elastic Actuator Design Using a Spiral Torsion Spring

This paper presents a novel series-elastic actuator (SEA) design that uses a spiral torsion spring to achieve drivetrain compliance in a compact and efficient mechanism. The SEA utilizes electromechanical actuation and is designed for use in the experimental biped robot KURMET for investigating dynamic maneuvers. Similar to helical torsion springs, spiral torsion springs are particularly applicable for legged robots because they preserve the rotational motion inherent in electric motors and articulated leg joints, but with less drivetrain backlash and unwanted coil interaction under load than helical torsion springs. The general spiral torsion spring design equations are presented in a form convenient for robot design, along with a detailed discussion of the mechanism surrounding the spring. Also, the SEA mechanism has a set of unidirectional hardstops that further improves the position control by allowing series-elasticity in only one rotational direction.

Design of Planar, Shape-Changing Rigid-Body Mechanisms for Morphing Aircraft Wings

This paper presents a procedure to synthesize planar rigid-body mechanisms, containing both prismatic and revolute joints, capable of approximating a shape change defined by a set of morphing curves in different positions. The existing mechanization process is extended specifically to enable the design of morphing aircraft wings. A portion of the closed-curve morphing chain that has minimal displacement is identified as the structural ground after the segmentation process. Because of the revolute joints placed at the endpoints of the ground section, the moving links of the fixed-end morphing chain need to be repositioned relative to each of the desired wing shapes so as to minimize the error in approximating them. With the introduction of prismatic joints, a building-block approach is employed to mechanize the fixed-end morphing chain. The blocks are located in an assembly position to generate a single degree-of-freedom (DOF) mechanism. Because of the additional constraints associated with prismatic joints compared to revolute joints, the size of the solution space is reduced, so random searches of the design space to find solution mechanisms are ineffective. A multi-objective genetic algorithm is employed instead to find a group of viable designs that tradeoff minimizing matching error with maximizing mechanical advantage. The procedure is demonstrated with a synthesis example of a 1-DOF mechanism approximating eight closed-curve wing profiles.

The effects of foot geometric properties on the gait of planar bipeds walking under HZD-based control

It has been hypothesized by many that foot design can influence gait. This idea was investigated in both simulation and hardware for the five-link, planar biped ERNIE controlled under the Hybrid Zero Dynamics paradigm. The effects of walking speed, foot radius, and foot center of curvature location on gait efficiency and kinematics were investigated in a full factorial study of gaits optimized using a work-based objective function. In most cases, the simulation correctly predicted the trends observed in hardware, indicating that simulation can be used for foot design. As expected, increasing walking speed decreased the energetic efficiency. The dominant effect of speed on joint kinematics was to alter the timing of the peak hip flexion. Increasing foot radius up to the length of the shank improved the energetic efficiency and increased the range of motion of the hip and knee joints. Shifting the foot center of curvature location forward altered the energetic efficiency in a manner that interacted with changes in foot radius. The energetically optimal foot center of curvature location was coincident with the shank for a large foot radius and shifted far in front of the shank for a small foot radius. In all cases, the forward shift increased the range of motion of the hip and knee joints. Therefore, a robot designer can achieve similar energetic benefits across a range of speeds with either a larger radius foot or a smaller radius foot whose center of curvature is located forward of the shank.