Control of Thruster-Assisted, Bipedal Legged Locomotion of the Harpy Robot

Fast constraint satisfaction, frontal dynamics stabilization, and avoiding fallovers in dynamic, bipedal walkers can be pretty challenging. The challenges include underactuation, vulnerability to external perturbations, and high computational complexity that arise when accounting for the system full-dynamics and environmental interactions. In this work, we study the potential roles of thrusters in addressing some of these locomotion challenges in bipedal robotics. We will introduce a thruster-assisted bipedal robot called Harpy. We will capitalize on Harpy’s unique design to propose an optimization-free approach to satisfy gait feasibility conditions. In this thruster-assisted legged locomotion, the reference trajectories can be manipulated to fulfill constraints brought on by ground contact and those prescribed for states and inputs. Unintended changes to the trajectories, especially those optimized to produce periodic orbits, can adversely affect gait stability and hybrid invariance. We will show our approach can still guarantee stability and hybrid invariance of the gaits by employing the thrusters in Harpy. We will also show that the thrusters can be leveraged to robustify the gaits by dodging fallovers or jumping over large obstacles.

Robert McNeill Alexander. 7 July 1934—21 March 2016

Neill Alexander graduated in natural sciences at the University of Cambridge in 1955. After a PhD at Cambridge and a lecturership at the University College of North Wales in Bangor, he was appointed to the chair of the Department of Pure and Applied Zoology at the University of Leeds in 1969. At that stage, he switched his research interests abruptly from fishes to the mechanics of legged locomotion. He conducted experiments with a variety of mammals, calculating forces, stresses and strains in muscle fibres, bones and tendons. His speciality became the application of mathematical models to animal locomotion, including repurposing the Froude number, devised by the Victorian engineer William Froude (FRS 1870) for use with ships, to estimate the speed of dinosaurs based on the spacing of their fossil footprints. Subsequent work included modelling the optimization of mammal performance and the minimization of energy costs. In 1992, following an announcement that London Zoo would have to close as a result of shortage of funds, Neill was appointed secretary of the Zoological Society of London. During the period of his secretaryship, the Society's finances recovered, with both its zoos (London and Whipsnade) breaking even in 1993 and the Society returning a surplus in each subsequent year. Neill was awarded the CBE in 2000. The National Portrait Gallery holds his portrait by John Arnison.

Cross-bridge mechanics estimated from skeletal muscles’ work-loop responses to impacts in legged locomotion

Legged locomotion has evolved as the most common form of terrestrial locomotion. When the leg makes contact with a solid surface, muscles absorb some of the shock-wave accelerations (impacts) that propagate through the body. We built a custom-made frame to which we fixated a rat (Rattus norvegicus, Wistar) muscle (m. gastrocnemius medialis and lateralis: GAS) for emulating an impact. We found that the fibre material of the muscle dissipates between 3.5 and $$23\,\upmu \hbox {J}$$ 23 μ J ranging from fresh, fully active to passive muscle material, respectively. Accordingly, the corresponding dissipated energy in a half-sarcomere ranges between 10.4 and $$68\,z\hbox {J}$$ 68 z J , respectively. At maximum activity, a single cross-bridge would, thus, dissipate 0.6% of the mechanical work available per ATP split per impact, and up to 16% energy in common, submaximal, activities. We also found the cross-bridge stiffness as low as $$2.2\,\hbox {pN}\,\hbox {nm}^{-1}$$ 2.2 pN nm - 1 , which can be explained by the Coulomb-actuating cross-bridge part dominating the sarcomere stiffness. Results of the study provide a deeper understanding of contractile dynamics during early ground contact in bouncy gait.

A bio-inspired robotic climbing robot to understand kinematic and morphological determinants for an optimal climbing gait

Robotic systems for complex tasks, such as search and rescue or exploration, are limited for wheeled designs, thus the study of legged locomotion for robotic applications has become increasingly important. To successfully navigate in regions with rough terrain, a robot must not only be able to negotiate obstacles, but also climb steep inclines. Following the principles of biomimetics, we developed a modular bio-inspired climbing robot, named X4, which mimics the lizard’s bauplan including an actuated spine, shoulders, and feet which interlock with the surface via claws. We included the ability to modify gait and hardware parameters and simultaneously collect data with the robot’s sensors on climbed distance, slip occurrence and efficiency. We first explored the speed-stability trade-off and its interaction with limb swing phase dynamics, finding a sigmoidal pattern of limb movement resulted in the greatest distance travelled. By modifying foot orientation, we found two optima for both speed and stability, suggesting multiple stable configurations. We varied spine and limb range of motion, again showing two possible optimum configurations, and finally varied the centre of pro- and retraction on climbing performance, showing an advantage for protracted limbs during the stride. We then stacked optimal regions of performance and show that combining optimal dynamic patterns with either foot angles or ROM configurations have the greatest performance, but further optima stacking resulted in a decrease in performance, suggesting complex interactions between kinematic parameters. The search of optimal parameter configurations might not only be beneficial to improve robotic in-field operations but may also further the study of the locomotive evolution of climbing of animals, like lizards or insects.

Kinematics of sea star legged locomotion

Sea stars have slower crawling and faster bouncing gaits. Both speed and oscillation amplitude increase during the transition from crawling to oscillating. In the bouncy gait, oscillating vertical velocities precede oscillating horizontal velocities by 90 degrees, as reflected by clockwise circular hodographs. Potential energy precedes horizontal kinetic energy by 9.6 degrees and so are nearly in phase. These phase relationships resemble terrestrial running gaits, except that podia are always on the ground. Kinetic and potential energy scale as mass1.1, with the change in kinetic energy consistently two orders of magnitude less, indicating that efficient exchange is not feasible. Frequency of the bouncy gait scales with mass−0.14, which is similar to continuously running vertebrates and indicates that gravitational forces are important. This scaling differs from the Hill model, in which scaling of muscle forces determine frequency. We propose a simple torque stabilized inverted pendulum (TS-IP) model to conceptualize the dynamics of this gait. The TS-IP model incorporates mathematics equivalent to an angular spring, but implemented by a nearly constant upward force generated by the podia in each step. That upward force is just larger than the force required to sustain the underwater weight of the sea star. Even though the bouncy gait is the rapid gait for these sea stars, the pace of movement is still very slow. In fact, the observed Froude numbers (10−2 to 10−3) are much lower than those typical of vertebrate locomotion and are as low or lower than those reported for slow walking fruit flies, which are the lowest values for pedestrian Froude numbers of which we are aware.

Quadrupedal Human-Assistive Robotic Platform (Q-HARP): Design, Control, and Preliminary Testing

With the rapid expansion of older adult populations around the world, mobility impairment is becoming an increasingly challenging issue. For the assistance of individuals with mobility impairments, there are two major types of tools in the current practice, including the passive (unpowered) walking aids (canes, walkers, rollators, etc.) and wheelchairs (powered and unpowered). Despite their extensive use, there are significant weaknesses that affect their effectiveness in daily use, especially when challenging uneven terrains are encountered. To address these issues, the authors developed a novel robotic platform intended for the assistance of mobility-challenged individuals. Unlike the existing assistive robots serving similar purposes, the proposed robot, namely, quadrupedal human-assistive robotic platform (Q-HARP), utilizes legged locomotion to provide an unprecedented potential to adapt to a wide variety of challenging terrains, many of which are common in people’s daily life (e.g., roadside curbs and the few steps leading to a front door). In this paper, the design of the robot is presented, including the overall structure of the robot and the design details of the actuated robotic leg joints. For the motion control of the robot, a joint trajectory generator is formulated, with the purpose of generating a stable walking gait to provide reliable support to its human user in the robot’s future application. The Q-HARP robot and its control system were experimentally tested, and the results demonstrated that the robot was able to provide a smooth gait during walking.

Intersegmental coordination of the central pattern generator via interleaved electrical and chemical synapses in zebrafish spinal cord

A significant component of the repetitive dynamics during locomotion in vertebrates is generated within the spinal cord. The legged locomotion of mammals is most likely controled by a hierarchical, multi-layer spinal network structure, while the axial circuitry generating the undulatory swimming motion of animals like lamprey is thought to have only a single layer in each segment. Recent experiments have suggested a hybrid network structure in zebrafish larvae in which two types of excitatory interneurons (V2a-I and V2a-II) both make first-order connections to the brain and last-order connections to the motor pool. These neurons are connected by electrical and chemical synapses across segments. Through computational modeling and an asymptotic perturbation approach we show that this interleaved interaction between the two neuron populations allows the spinal network to quickly establish the correct activation sequence of the segments when starting from random initial conditions and to reduce the dependence of the intersegmental phase difference (ISPD) of the oscillations on the swimming frequency. The latter reduces the frequency dependence of the waveform of the swimming motion. In the model the reduced frequency dependence is largely due to the different impact of chemical and electrical synapses on the ISPD and to the significant spike-frequency adaptation that has been observed experimentally in V2a-II neurons, but not in V2a-I neurons. Our model makes experimentally testable predictions and points to a benefit of the hybrid structure for undulatory locomotion that may not be relevant for legged locomotion.

Generation of Direct-, Retrograde-, and Source-Wave Gaits in Multi-Legged Locomotion in a Decentralized Manner via Embodied Sensorimotor Interaction

Multi-legged animals show several types of ipsilateral interlimb coordination. Millipedes use a direct-wave gait, in which the swing leg movements propagate from posterior to anterior. In contrast, centipedes use a retrograde-wave gait, in which the swing leg movements propagate from anterior to posterior. Interestingly, when millipedes walk in a specific way, both direct and retrograde waves of the swing leg movements appear with the waves' source, which we call the source-wave gait. However, the gait generation mechanism is still unclear because of the complex nature of the interaction between neural control and dynamic body systems. The present study used a simple model to understand the mechanism better, primarily how local sensory feedback affects multi-legged locomotion. The model comprises a multi-legged body and its locomotion control system using biologically inspired oscillators with local sensory feedback, phase resetting. Each oscillator controls each leg independently. Our simulation produced the above three types of animal gaits. These gaits are not predesigned but emerge through the interaction between the neural control and dynamic body systems through sensory feedback (embodied sensorimotor interaction) in a decentralized manner. The analytical description of these gaits' solution and stability clarifies the embodied sensorimotor interaction's functional roles in the interlimb coordination.

Autonomous speed adaptation by a muscle-driven hind leg robot modeled on a cat without intervention from brain

This study aims to design a nervous system model to drive the realistic muscle-driven legs for the locomotion of a quadruped robot. We evaluate our proposed nervous system model with a hind leg simulated model and robot. We apply a two-level central pattern generator for each leg, which generates locomotion rhythms and reproduces cat-like leg trajectories by driving different sets of the muscles at any timing during one cycle of moving the leg. The central pattern generator receives sensory feedback from leg loading. A cat simulated model and a robot with two hind legs, each with three joints driven by six muscle models, are controlled by our nervous system model. Even though their hind legs are forced backward at a wide range of speeds, they can adapt to the speed variation by autonomously adjusting its stride and cyclic duration without changing any parameters or receiving any descending inputs. In addition to the autonomous speed adaptation, the cat hind leg robot switched from a trot-like gait to a gallop-like gait while speeding up. These features can be observed in existing animal locomotion tests. These results demonstrate that our nervous system is useful as a valid and practical legged locomotion controller.