Neural Control of Interlimb Oscillations II. Biped and Quadruped Gaits and Bifurications

Behavioral data concerning animal and human gaits and gait transitions are simulated as emergent properties of a central pattern generator (CPG) model. The CPG model is a version of the Ellias-Grossberg oscillator. Its neurons obey Hodgkin-Huxley type equations whose excitatory signals operate on a faster time scale than their inhibitory signals in a recurrent on-center off-surround anatomy. A descending command or GO signal activates the gaits and triggers gait transitions as its amplitude increases. A single model CPG can generate both in-phase and anti-phase oscillations at different GO amplitudes. Phase transition from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases. Quadruped vertebrate gaits, including the amble, the walk, all three pairwise gaits (trot, pace, and gallop), and the pronk are simulated using this property. Rapid gait transitions are simulated in the order walk, trot, pace, and gallop that occurs in the cat, along with the observed increase in oscillation frequency. Precise control of quadruped gait switching uses GO-dependent. modulation of inhibitory interactions, which generates a different functional anatomy at different arousal levels. The primary human gaits (the walk and the run) and elephant gaits (the amble and the walk) are simulated, without modulation, by oscillations with the same phase relationships but different waveform shapes at different GO signal levels, much as the duty cycles of the feet are longer in the walk than in the run. Relevant neural data from spinal cord, globus palliclus, and motor cortex, among other structures, are discussedArmy Research Office (DAAL03-88-K-0088); Advanced Research Projects Agency (90-0083); National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-92-J-1309); Air Force Office of Scientific Research (F49620-92-J-0499, F49620-92-J-0225, 90-0128

Neural Control of Interlimb Coordination and Gait Timing in Bipeds and Quadrupeds

1) A large body of behavioral data conceming animal and human gaits and gait transitions is simulated as emergent properties of a central pattern generator (CPG) model. The CPG model incorporates neurons obeying Hodgkin-Huxley type dynamics that interact via an on-center off-surround anatomy whose excitatory signals operate on a faster time scale than their inhibitory signals. A descending cornmand or arousal signal called a GO signal activates the gaits and controL their transitions. The GO signal and the CPG model are compared with neural data from globus pallidus and spinal cord, among other brain structures. 2) Data from human bimanual finger coordination tasks are simulated in which anti-phase oscillations at low frequencies spontaneously switch to in-phase oscillations at high frequencies, in-phase oscillations can be performed both at low and high frequencies, phase fluctuations occur at the anti-phase in-phase transition, and a "seagull effect" of larger errors occurs at intermediate phases. When driven by environmental patterns with intermediate phase relationships, the model's output exhibits a tendency to slip toward purely in-phase and anti-phase relationships as observed in humans subjects. 3) Quadruped vertebrate gaits, including the amble, the walk, all three pairwise gaits (trot, pace, and gallop) and the pronk are simulated. Rapid gait transitions are simulated in the order--walk, trot, pace, and gallop--that occurs in the cat, along with the observed increase in oscillation frequency. 4) Precise control of quadruped gait switching is achieved in the model by using GO-dependent modulation of the model's inhibitory interactions. This generates a different functional connectivity in a single CPG at different arousal levels. Such task-specific modulation of functional connectivity in neural pattern generators has been experimentally reported in invertebrates. Phase-dependent modulation of reflex gain has been observed in cats. A role for state-dependent modulation is herein predicted to occur in vertebrates for precise control of phase transitions from one gait to another. 5) The primary human gaits (the walk and the run) and elephant gaits (the amble and the walk) are sirnulated. Although these two gaits are qualitatively different, they both have the same limb order and may exhibit oscillation frequencies that overlap. The CPG model simulates the walk and the run by generating oscillations which exhibit the same phase relationships. but qualitatively different waveform shapes, at different GO signal levels. The fraction of each cycle that activity is above threshold quantitatively distinguishes the two gaits, much as the duty cycles of the feet are longer in the walk than in the run. 6) A key model properly concerns the ability of a single model CPG, that obeys a fixed set of opponent processing equations to generate both in-phase and anti-phase oscillations at different arousal levels. Phase transitions from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases.Air Force Office of Scientific Research (90-0128, F49620-92-J-0225, 90-0175); National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-92-J-1309); Army Research Office (DAAL03-88-K-0088); Advanced Research Projects Agency (90-0083

BIOMECHANICS OF TERRESTRIAL LOCOMOTION: ASYMMETRIC OCTOPEDAL AND QUADRUPEDAL GAITS

The main goal of this dissertation is to investigate the biomechanics of octopedal and quadrupedal locomotion in terrestrial animals, common determinants, advantages and limits, in particular of the asymmetric gaits. Two different approach have been chosen: i) a kinematic study of a terrestrial spider, the Brazilian giant tawny-red tarantula, an octopods predator species that hide in burrows, ambush and rapidly bounce the prey with a sprint, and ii) a comparative study of the two types of gallop of the cursorial terrestrial mammals. Eight-legs locomotion has been one of the first travelling modes on land, and spiders display one of the most versatile locomotor repertoire: they move at slow and fast speed, forward-backward-sideways, they climb and even jump, both on firm terrain and from the water surface. Spiders can walk in the two senses at the same speed, just by reversing their diagonal footfall scheme. They turn on the spot like an armoured tank, with opposite direction of the two treads of limbs. Also, the high number of limbs ensures an increased locomotor versatility on uneven and rough terrains, particularly in the likely unawareness of each endpoint location on the ground. The aims of this first part were: i) identifying the principal octopod gaits, ii) calculating the mechanical external and internal work at the different speeds/gaits, iii) assessing any tendency to exchange potential and kinetic energy of the body centre of mass, as in pendulum-like gaits, and iv) evaluating how spiders\u2019 mechanical performance and variables allometrically compare to other species. Another question was: can the octopod gaits be considered as different combinations of two quadrupeds\u2019 locomotion? In this investigation we used inverse dynamics to study the locomotor performance of a terrestrial spider. 9 reflective markers have been placed on the tip of the 8 legs and on the cephalothorax, and their position recorded at a frequency of 50 Hz and digitized through a motion analysis system. Data have been processed using LabView (National Instruments, USA) specific development. The 3D trajectories of the body centre of mass in local coordinates, as during locomotion on a treadmill, have been calculated by applying a mathematical method based on the Fourier analysis of the three coordinates of the centre of mass (COM) over time. Two main gaits, a slow and a fast one characterised by distinctive 3D trajectories of COM, have been identified. The calculated total mechanical work (= external+internal) and metabolic data from the literature allowed estimating the locomotion efficiency of this species, which resulted less than 4%. Octopod gait pattern due to alternating limb support, which generates asymmetrical COM trajectories and a small but consistent energy transfer between potential and kinetic energies of COM, can be considered as formed by two subsequent quadrupeds, where the first two pairs of feet (1 and 2) are the fore and the hind feet of the first quadruped, and the third and fourth pairs are the fore and hind feet of the second quadruped. The two quadrupeds are almost in phase, being the first and third pairs synchronised in their movements as well as the second and fourth. Octopedal locomotion exhibits two main gaits, neither of which incorporating a flight phase, characterised by a consistent limb pattern and a small but remarkable energy recovery index. Gallop has been chosen as model of asymmetric cursorial locomotion in quadrupeds. In transverse gallop the placement of the second hind foot is followed by that of the contralateral forefoot, while in rotary gallop is followed by the ipsilateral forefoot, and the sequence of footfalls appears to rotate around the body. The question are: why two models of gallop? Are they specie-specific? Which are the biomechanical determinants of the choice between transverse and rotary gallop? Aims of this part of the research were: i) assess, when possible, the specie-specificity of the gallop type in different cursorial mammal species, ii) phylogenetically classify the investigated species, iii) Made a comparative analysis based on morphological, physiological and environmental differences. 351 filmed sequences have been analysed to assess the gallop type of 89 investigated mammal species belonging to Carnivora, Artiodactyla and Perissodactyla orders. 23 biometrical, ecological and physiological parameters have been collected for each species both from literature data and from experimental measures. Most of the species showed only one kind of gallop: transverse (42%) or rotary (39%), while some species performed rotary gallop only at high speed (19%). In a multivariate factorial analysis the first principal component (PC), which accounted for 40% of the total variance, was positively correlated to the relative speed and negatively correlated to size and body mass. The second PC was correlated to the ratio between autopodial and zygopodial limb segments. Large size and longer proximal limb segments resulted associated to transverse gallop, while rotary and speed dependent species showed higher metacarpus/humerus and metatarsus/femur length ratio and faster relative speeds. The maximum angular excursion resulted proportional to the maximum Froude number, and significantly higher in rotary galloper. The gait pattern analysis provided significant differences between transverse and rotary gallop in fore and hind duty factor, and in duration of the fore contact. Our results assessed that a typical gallop gait is adopted by a large number of mammal species, and indicated that the gallop pattern depends on diverse environmental, morphometrical and biomechanical characters. Even if mammals and spiders can be considered far and different worlds, we can recognize common pattern of locomotion. The quadruped gaits have been modelled as the combination of two biped gaits with some difference in the phase-cycle, in the same way, we described the octopods gaits as the combination of two quadruped gaits in series. In conclusion, this work shed light on some aspects of octopedal and quadrupedal asymmetric gaits, opening to the raising of new questions and new perspective of research

Omnidirectional Control of the Hexapod Robot TigerBug

TigerBug is a six legged, hexapod robot built and designed by students in the Rochester Institute of Technology\u27s (RIT) Multi Agent Bio-Robotics Laboratory (MABL). TigerBug is comprised of 18 servo motors, 3 degrees of freedom (DOF) per leg, supported by carbon fiber wrapped foam legs placed in a circular pattern around its hexagon shaped body. In order to control such a complex system, much research has been done in the field of kinematics. There exist two derivations of kinematic solutions, forward and inverse. The forward kinematic (FK) solution tends to be much simpler than its inverse kinematic (IK) counterpart. There has been many methods developed to quickly, and efficiently solve the IK in order to control the position and orientation of a robot. This thesis details the process of developing the IK solution and two gait algorithms for TigerBug. The IK solution was developed by first solving for the FK solution of TigerBug using Denavit-Hartenberg (DH) Parameters. After the FK solution was solved, differentials were applied to each equation in order to solve for the IK solution. Once the IK solution was tested, a fixed gait algorithm was developed in order to understand basic motion control of hexapod locomotion. Once the fixed gait was implemented successfully a rule-based free gait algorithm was developed. The rule-based free gait was accomplished using the rule set governed by restrictiveness to determine when leg state transitions were to occur, as described in the literature. Once implemented, the different combinations of gait parameters were tested for quickness of convergence and efficiency to determine the most optimal set of walking parameters for TigerBug

Bio-inspired Dynamic Control Systems with Time Delays

The world around us exhibits a rich and ever changing environment of startling, bewildering and fascinating complexity. Almost everything is never as simple as it seems, but through the chaos we may catch fleeting glimpses of the mechanisms within. Throughout the history of human endeavour we have mimicked nature to harness it for our own ends. Our attempts to develop truly autonomous and intelligent machines have however struggled with the limitations of our human ability. This has encouraged some to shirk this responsibility and instead model biological processes and systems to do it for us. This Thesis explores the introduction of continuous time delays into biologically inspired dynamic control systems. We seek to exploit rich temporal dynamics found in physical and biological systems for modelling complex or adaptive behaviour through the artificial evolution of networks to control robots. Throughout, arguments have been presented for the modelling of delays not only to better represent key facets of physical and biological systems, but to increase the computational potential of such systems for the synthesis of control. The thorough investigation of the dynamics of small delayed networks with a wide range of time delays has been undertaken, with a detailed mathematical description of the fixed points of the system and possible oscillatory modes developed to fully describe the behaviour of a single node. Exploration of the behaviour for even small delayed networks illustrates the range of complex behaviour possible and guides the development of interesting solutions. To further exploit the potential of the rich dynamics in such systems, a novel approach to the 3D simulation of locomotory robots has been developed focussing on minimising the computational cost. To verify this simulation tool a simple quadruped robot was developed and the motion of the robot when undergoing a manually designed gait evaluated. The results displayed a high degree of agreement between the simulation and laser tracker data, verifying the accuracy of the model developed. A new model of a dynamic system which includes continuous time delays has been introduced, and its utility demonstrated in the evolution of networks for the solution of simple learning behaviours. A range of methods has been developed for determining the time delays, including the novel concept of representing the time delays as related to the distance between nodes in a spatial representation of the network. The application of these tools to a range of examples has been explored, from Gene Regulatory Networks (GRNs) to robot control and neural networks. The performance of these systems has been compared and contrasted with the efficacy of evolutionary runs for the same task over the whole range of network and delay types. It has been shown that delayed dynamic neural systems are at least as capable as traditional Continuous Time Recurrent Neural Networks (CTRNNs) and show significant performance improvements in the control of robot gaits. Experiments in adaptive behaviour, where there is not such a direct link between the enhanced system dynamics and performance, showed no such discernible improvement. Whilst we hypothesise that the ability of such delayed networks to generate switched pattern generating nodes may be useful in Evolutionary Robotics (ER) this was not borne out here. The spatial representation of delays was shown to be more efficient for larger networks, however these techniques restricted the search to lower complexity solutions or led to a significant falloff as the network structure becomes more complex. This would suggest that for anything other than a simple genotype, the direct method for encoding delays is likely most appropriate. With proven benefits for robot locomotion and the open potential for adaptive behaviour delayed dynamic systems for evolved control remain an interesting and promising field in complex systems research

Fast biped walking with a neuronal controller and physical computation

Biped walking remains a difficult problem and robot models can greatly {facilitate} our understanding of the underlying biomechanical principles as well as their neuronal control. The goal of this study is to specifically demonstrate that stable biped walking can be achieved by combining the physical properties of the walking robot with a small, reflex-based neuronal network, which is governed mainly by local sensor signals. This study shows that human-like gaits emerge without {specific} position or trajectory control and that the walker is able to compensate small disturbances through its own dynamical properties. The reflexive controller used here has the following characteristics, which are different from earlier approaches: (1) Control is mainly local. Hence, it uses only two signals (AEA=Anterior Extreme Angle and GC=Ground Contact) which operate at the inter-joint level. All other signals operate only at single joints. (2) Neither position control nor trajectory tracking control is used. Instead, the approximate nature of the local reflexes on each joint allows the robot mechanics itself (e.g., its passive dynamics) to contribute substantially to the overall gait trajectory computation. (3) The motor control scheme used in the local reflexes of our robot is more straightforward and has more biological plausibility than that of other robots, because the outputs of the motorneurons in our reflexive controller are directly driving the motors of the joints, rather than working as references for position or velocity control. As a consequence, the neural controller and the robot mechanics are closely coupled as a neuro-mechanical system and this study emphasises that dynamically stable biped walking gaits emerge from the coupling between neural computation and physical computation. This is demonstrated by different walking experiments using two real robot as well as by a Poincar\'{e} map analysis applied on a model of the robot in order to assess its stability. In addition, this neuronal control structure allows the use of a policy gradient reinforcement learning algorithm to tune the parameters of the neurons in real-time, during walking. This way the robot can reach a record-breaking walking speed of 3.5 leg-lengths per second after only a few minutes of online learning, which is even comparable to the fastest relative speed of human walking