Central pattern generators for bipedal locomotion

Golubitsky, Stewart, Buono and Collins proposed two models for the achitecture of central pattern generators (CPGs): one for bipeds (which we call leg) and one for quadrupeds (which we call quad). In this paper we use symmetry techniques to classify the possible spatiotemporal symmetries of periodic solutions that can exist in leg (there are 10 nontrivial types) and we explore the possibility that coordinated arm/leg rhythms can be understood, on the CPG level, by a small breaking of the symmetry in quad, which leads to a third CPG architecture arm. Rhythms produced by leg correspond to the bipedal gaits of walk, run, two-legged hop, two-legged jump, skip, gallop, asymmetric hop, and one-legged hop. We show that breaking the symmetry between fore and hind limbs in quad, which yields the CPG arm, leads to periodic solution types whose associated leg rhythms correspond to seven of the eight leg gaits found in leg; the missing biped gait is the asymmetric hop. However, when arm/leg coordination rhythms are considered, we find the correct rhythms only for the biped gaits of two-legged hop, run, and gallop. In particular, the biped gait walk, along with its arm rhythms, cannot be obtained by a small breaking of symmetry of any quadruped gait supported by quad.     

Emergence of adaptability to time delay in bipedal locomotion

Based on neurophysiological evidence, theoretical studies have shown that locomotion is generated by mutual entrainment between the oscillatory activities of central pattern generators (CPGs) and body motion. However, it has also been shown that the time delay in the sensorimotor loop can destabilize mutual entrainment and result in the failure to walk. In this study, a new mechanism called flexible-phase locking is proposed to overcome the time delay. It is realized by employing the Bonhoeffer–Van der Pol formalism – well known as a physiologically faithful neuronal model – for neurons in the CPG. The formalism states that neurons modulate their phase according to the delay so that mutual entrainment is stabilized. Flexible-phase locking derives from the phase dynamics related to an asymptotically stable limit cycle of the neuron. The effectiveness of the mechanism is verified by computer simulations of a bipedal locomotion model.     

Real-time inverse kinematics and inverse dynamics for lower limb applications using OpenSim

Real-time estimation of joint angles and moments can be used for rapid evaluation in clinical, sport, and rehabilitation contexts. However, real-time calculation of kinematics and kinetics is currently based on approximate solutions or generic anatomical models. We present a real-time system based on OpenSim solving inverse kinematics and dynamics without simplifications at 2000 frame per seconds with less than 31.5 ms of delay. We describe the software architecture, sensitivity analyses to minimise delays and errors, and compare offline and real-time results. This system has the potential to strongly impact current rehabilitation practices enabling the use of personalised musculoskeletal models in real-time.     

Modeling locomotion of a soft-bodied arthropod using inverse dynamics

Most bio-inspired robots have been based on animals with jointed, stiff skeletons. There is now an increasing interest in mimicking the robust performance of animals in natural environments by incorporating compliant materials into the locomotory system. However, the mechanics of moving, highly conformable structures are particularly difficult to predict. This paper proposes a planar, extensible-link model for the soft-bodied tobacco hornworm caterpillar, Manduca sexta, to provide insight for biologists and engineers studying locomotion by highly deformable animals and caterpillar-like robots. Using inverse dynamics to process experimentally acquired point-tracking data, ground reaction forces and internal forces were determined for a crawling caterpillar. Computed ground reaction forces were compared to experimental data to validate the model. The results show that a system of linked extendable joints can faithfully describe the general form and magnitude of the contact forces produced by a crawling caterpillar. Furthermore, the model can be used to compute internal forces that cannot be measured experimentally. It is predicted that between different body segments in stance phase the body is mostly kept in tension and that compression only occurs during the swing phase when the prolegs release their grip. This finding supports a recently proposed mechanism for locomotion by soft animals in which the substrate transfers compressive forces from one part of the body to another (the environmental skeleton) thereby minimizing the need for hydrostatic stiffening. The model also provides a new means to characterize and test control strategies used in caterpillar crawling and soft robot locomotion.     

A model of bipedal locomotion on compliant legs.

Simple mathematical models capable of walking or running are used to compare the merits of bipedal gaits. Stride length, duty factor (the fraction of the stride, for which the foot is on the ground) and the pattern of force on the ground are varied, and the optimum gait is deemed to be the one that minimizes the positive work that the muscles must perform, per unit distance travelled. Even the simplest model, whose legs have neither mass nor elastic compliance, predicts the changes of duty factor and force pattern that people make as they increase their speed of walking. It predicts a sudden change to running at a critical speed, but this is much faster than the speed at which people make the change. When elastic compliance is incorporated in the model, unnaturally fast walking becomes uncompetitive. However, a slow run with very brief foot contact becomes the optimum gait at low speeds, at which people would walk, unless severe energy dissipation occurs in the compliance. A model whose legs have mass as well as elastic compliance predicts well the relationship between speed and stride length in human walking.     

Forward dynamic simulation of bipedal walking in the Japanese macaque: investigation of causal relationships among limb kinematics, speed, and energetics of bipedal locomotion in a nonhuman primate

Japanese macaques that have been trained for monkey performances exhibit a remarkable ability to walk bipedally. In this study, we dynamically reconstructed bipedal walking of the Japanese macaque to investigate causal relationships among limb kinematics, speed, and energetics, with a view to understanding the mechanisms underlying the evolution of human bipedalism. We constructed a two-dimensional macaque musculoskeletal model consisting of nine rigid links and eight principal muscles. To generate locomotion, we used a trajectory-tracking control law, the reference trajectories of which were obtained experimentally. Using this framework, we evaluated the effects of changes in cycle duration and gait kinematics on locomotor efficiency. The energetic cost of locomotion was estimated based on the calculation of mechanical energy generated by muscles. Our results demonstrated that the mass-specific metabolic cost of transport decreased as speed increased in bipedal walking of the Japanese macaque. Furthermore, the cost of transport in bipedal walking was reduced when vertical displacement of the hip joint was virtually modified in the simulation to be more humanlike. Human vertical fluctuations in the body's center of mass actually contributed to energy savings via an inverted pendulum mechanism.     

Generation of human bipedal locomotion by a bio-mimetic neuro-musculo-skeletal model

To emulate the actual neuro-control mechanism of human bipedal locomotion, an anatomically and physiologically based neuro-musculo-skeletal model is developed. The human musculo-skeletal system is constructed as seven rigid links in a sagittal plane, with a total of nine principal muscles. The nervous system consists of an alpha motoneuron and proprioceptors such as a muscle spindle and a Golgi tendon organ for each muscle. At the motoneurons, feedback signals from the proprioceptors are integrated with the signal induced by foot–ground contact and input from the rhythm pattern generator; a muscle activation signal is produced accordingly. Weights of connection in the neural network are optimized using a genetic algorithm, thus maximizing walking distance and minimizing energy consumption. The generated walking pattern is in remarkably good agreement with that of actual human walking, indicating that the locomotory pattern could be generated automatically, according to the musculo-skeletal structures and the connections of the peripheral nervous system, particularly due to the reciprocal innervation in the muscle spindles. Using the proposed model, the flow of sensory-motor information during locomotion is estimated and a possible neuro-control mechanism is discussed. Received: 03 December 1998 / Accepted in revised form: 09 June 2000     

Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment

A new principle of sensorimotor control of legged locomotion in an unpredictable environment is proposed on the basis of neurophysiological knowledge and a theory of nonlinear dynamics. Stable and flexible locomotion is realized as a global limit cycle generated by a global entrainment between the rhythmic activities of a nervous system composed of coupled neural oscillators and the rhythmic movements of a musculo-skeletal system including interaction with its environment. Coordinated movements are generated not by slaving to an explicit representation of the precise trajectories of the movement of each part but by dynamic interactions among the nervous system, the musculo-skeletal system and the environment. The performance of a bipedal model based on the above principle was investigated by computer simulation. Walking movements stable to mechanical perturbations and to environmental changes were obtained. Moreover, the model generated not only the walking movement but also the running movement by changing a single parameter nonspecific to the movement. The transitions between the gait patterns occurred with hysteresis.     

Chimpanzee bipedal locomotion in the Gombe National Park,East Africa

An adult male chimpanzee in the natural habitat has been observed to walk predominantly bipedally after a total forelimb paralysis in 1966. The major differences from previously described bipedal chimpanzee gait are (1) one third of the femoral extension is posterior to the hip joint in propulsion, (2) excursion of the swinging foot is close to midline, due to adduction of the lower hindlimb in swing and propulsive phases, (3) depressed pelvic tilt is on the side of the swinging limb, (4) thoracic vertebrae rotate and are vertical and erect, and (5) there is only a moderate lateral sway of the midline. This locomotory complex is interpreted as individual variability and suggests an evolutionary model for the origin of hominid bipedal locomotion.     

Limb morphology,bipedal gait,and the energetics of hominid locomotion

How viable is the argument that increased locomotor efficiency was an important agent in the origin of hominid bipedalism? This study reviews data from the literature on the cost of human bipedal walking and running and compares it to data on quadrupedal mammals including several non-human primate species. Literature data comparing the cost of bipedal and quadrupedal locomotion in trained capuchin monkeys and chimpanzees are also considered. It is concluded that increased energetic efficiency would not have accrued to early bipeds. Presumably, however, selection for improved efficiency in the bipedal stance would have occurred once the transition was made. Would such a process have included selection for increased limb length? Data on the cost of locomotion vs. limb length reveal no significant relationship between these variables in 21 species of mammals or in human walking or running. © 1996 Wiley-Liss, Inc.     

Presenting joint kinematics of human locomotion using phase plane portraits and Poincaré maps

Additional graphical tools are needed to better visualize the joint kinematics of human locomotion. Standard plots in which the joint displacements are plotted against time or percent gait cycle do not provide sufficient information about the dynamics of the system. In this article, a study based on the two graphical tools of nonlinear dynamics to visualize the steady-state kinematics of human gait is presented. An experimental setup was developed to acquire the necessary data for application of the techniques. Twenty young adults, whose medical histories are free of gait pathology, were tested. Computerized electrogoniometers and foot switches were used to measure the kinematic data of the lower extremities and capture four instants of the gait cycle: heel strike, foot flat, heel off, and toe off. Phase plane portraits of each joint were constructed for the sagittal plane by plotting angular velocity against angular displacement. Poincaré maps were obtained by periodically sampling the joint profiles at toe off and plotting the ith iterate against the (i + 1)th one. Phase plane portraits are useful in monitoring the variations of joint velocity and position on the same graph in a more compact form. Poincaré maps are effective in differentiating steady gait from transient locomotion.     

Variations in blood supply allocations for quadrupedal and for bipedal posture and locomotion

Hemodynamics and orthodynamics were investigated in quadrupeds (dogs) and in bipeds (humans). The subjects were investigated at rest in supine or lateral posture, in quadrupedal and then in bipedal posture, and during locomotion. Quadrupedalism in humans was with subjects on their hands and knees. Bipedalism in dogs was on hindlimbs with the forelimbs held by a technician. Blood flow in the main arteries of the body (aorta, external and internal carotid, subclavian, and femoral) was measured by sonography. Positional variations between the main bones of the body were determined from X-rays. This study investigated the reallocation of blood supply to different regions of the body when it switches from quadrupedal to bipedal posture and locomotion. Compared with resting posture, the principal findings are 1) cardiac output shows a minimal increase for humans in bipedal stance and a noticeable increase for dogs as well as humans in quadrupedal stance; 2) quadrupedal stance in humans and dogs and bipedal stance in dogs require increased blood supply to the muscles of the neck, back, and limbs, while human bipedal stance requires none of these; 3) cerebral blood flow (internal carotid) in humans did not change as a result of bipedal posture or locomotion, but showed a noticeable drop in quadrupedal posture and an even further drop in quadrupedal locomotion. The conclusion is that erect posture and encephalization produced a noticeable readjustment and reallocation of blood flow among the different regions of the body: This consisted in shifting a large volume of blood supply from the musculature to the human brain.     

Bird terrestrial locomotion as revealed by 3D kinematics

Most birds use at least two modes of locomotion: flying and walking (terrestrial locomotion). Whereas the wings and tail are used for flying, the legs are mainly used for walking. The role of other body segments remains, however, poorly understood. In this study, we examine the kinematics of the head, the trunk, and the legs during terrestrial locomotion in the quail (Coturnix coturnix). Despite the trunk representing about 70% of the total body mass, its function in locomotion has received little scientific interest to date. This prompted us to focus on its role in terrestrial locomotion. We used high-speed video fluoroscopic recordings of quails walking at voluntary speeds on a trackway. Dorso-ventral and lateral views of the motion of the skeletal elements were recorded successively and reconstructed in three dimensions using a novel method based on the temporal synchronisation of both views. An analysis of the trajectories of the body parts and their coordination showed that the trunk plays an important role during walking. Moreover, two sub-systems participate in the gait kinematics: (i) the integrated 3D motion of the trunk and thighs allows for the adjustment of the path of the centre of mass; (ii) the motion of distal limbs transforms the alternating forward motion of the feet into a continuous forward motion at the knee and thus assures propulsion. Finally, head bobbing appears qualitatively synchronised to the movements of the trunk. An important role for the thigh muscles in generating the 3D motion of the trunk is suggested by an analysis of the pelvic anatomy.     

Kinematic analysis of bipedal locomotion of a Japanese macaque that lost its forearms due to congenital malformation

Spontaneously acquired bipedal locomotion of an untrained Japanese monkey (Macaca fuscata) is measured and compared with the elaborated bipedal locomotion of highly trained monkeys to assess the natural ability of a quadrupedal primate to walk bipedally. The subject acquired bipedalism by himself because of the loss of his forearms and hands due to congenital malformation. Two other subjects are performing monkeys that have been extensively trained for bipedal posture and locomotion. We videotaped their bipedal locomotion with two cameras in a lateral view and calculated joint angles (hip, knee, and ankle) and inertial angle of the trunk from the digitized joint positions. The results show that all joints are relatively more flexed in the untrained monkey. Moreover, it is noted that the ankle is less plantar flexed and the knee is more flexed in mid-to-late stance phase in the untrained monkey, suggesting that the trunk is not lifted up to store potential energy. In the trained monkeys, the joints are extended to bring the trunk as high as possible in the stance phase, and then stored potential energy is exchanged for kinetic energy to move forward. The efficient inverted pendulum mechanism seems to be absent in the untrained monkeys locomotion, implying that acquisition of such efficient bipedal locomotion is not a spontaneous ability for a Japanese monkey. Rather, it is probably a special skill that can only be acquired through artificial training for an inherently quadrupedal primate.This revised version was published online in April 2005 with corrections to the cover date of the issue.