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

Evolved embodied phase coordination enables robust quadruped robot locomotion

Overcoming robotics challenges in the real world requires resilient control systems capable of handling a multitude of environments and unforeseen events. Evolutionary optimization using simulations is a promising way to automatically design such control systems, however, if the disparity between simulation and the real world becomes too large, the optimization process may result in dysfunctional real-world behaviors. In this paper, we address this challenge by considering embodied phase coordination in the evolutionary optimization of a quadruped robot controller based on central pattern generators. With this method, leg phases, and indirectly also inter-leg coordination, are influenced by sensor feedback.By comparing two very similar control systems we gain insight into how the sensory feedback approach affects the evolved parameters of the control system, and how the performances differs in simulation, in transferal to the real world, and to different real-world environments. We show that evolution enables the design of a control system with embodied phase coordination which is more complex than previously seen approaches, and that this system is capable of controlling a real-world multi-jointed quadruped robot.The approach reduces the performance discrepancy between simulation and the real world, and displays robustness towards new environments.Comment: 9 page

Evolution of central pattern generators for the control of a five-link bipedal walking mechanism

Central pattern generators (CPGs), with a basis is neurophysiological studies, are a type of neural network for the generation of rhythmic motion. While CPGs are being increasingly used in robot control, most applications are hand-tuned for a specific task and it is acknowledged in the field that generic methods and design principles for creating individual networks for a given task are lacking. This study presents an approach where the connectivity and oscillatory parameters of a CPG network are determined by an evolutionary algorithm with fitness evaluations in a realistic simulation with accurate physics. We apply this technique to a five-link planar walking mechanism to demonstrate its feasibility and performance. In addition, to see whether results from simulation can be acceptably transferred to real robot hardware, the best evolved CPG network is also tested on a real mechanism. Our results also confirm that the biologically inspired CPG model is well suited for legged locomotion, since a diverse manifestation of networks have been observed to succeed in fitness simulations during evolution.Comment: 11 pages, 9 figures; substantial revision of content, organization, and quantitative result

Body randomization reduces the sim-to-real gap for compliant quadruped locomotion

Designing controllers for compliant, underactuated robots is challenging and usually requires a learning procedure. Learning robotic control in simulated environments can speed up the process whilst lowering risk of physical damage. Since perfect simulations are unfeasible, several techniques are used to improve transfer to the real world. Here, we investigate the impact of randomizing body parameters during learning of CPG controllers in simulation. The controllers are evaluated on our physical quadruped robot. We find that body randomization in simulation increases chances of finding gaits that function well on the real robot

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

Üner Tan Syndrome: Review and Emergence of Human Quadrupedalism in Self-Organization,\ud Attractors and Evolutionary Perspectives\ud

The first man reported in the world literature exhibiting habitual quadrupedal locomotion was discovered by a British traveler and writer on the famous Baghdat road near Havsa/Samsun on the middle Black-Sea coast of Turkey (Childs, 1917). Interestingly, no single case with human quadrupedalism was reported in the scientific literature after Child's first description in 1917 until the first report on the Uner Tan syndrome (UTS: quadrupedalism, mental retardation, and impaired speech or no speech)in 2005 (Tan, 2005, 2006). Between 2005 and 2010, 10 families exhibiting the syndrome were discovered in Turkey with 33 cases: 14 women (42.4%) and 19 men (57.6%). Including a few cases from other countries, there were 25 men (64.1%)and 14 women (35.9%). The number of men significantly exceeded the number of women (p < .05). Genetics alone did not seem to be informative for the origins of many syndromes, including the Uner Tan syndrome. From the viewpoint of dynamical systems theory, there may not be a single factor including the neural and/or genetic codes that predetermines the emergence of the human quadrupedalism.Rather, it may involve a self-organization process, consisting of many decentralized and local interactions among neuronal, genetic, and environmental subsystems. The most remarkable characteristic of the UTS, the diagonal-sequence quadrupedalism is well developed in primates. The evolutionarily advantage of this gait is not known. However, there seems to be an evolutionarily advantage of this type of locomotion for primate evolution, with regard to the emergence of complex neural circuits with related highly complex structures. Namely, only primates with diagonal-sequence quadrupedal locomotion followed an evolution favoring larger brains, highly developed cognitive abilities with hand skills, and language, with erect posture and bipedal locomotion, creating the unity of human being. It was suggested that UTS may be considered a further example for Darwinian diseases, which may be associated with an evolutionary understanding of the disorders using evolutionary principles, such as the natural selection. On the other hand, the human quadrupedalism was proposed to be a phenotypic example of evolution of reverse, i.e., the reacquisition by derived populations of the same character states as those of ancestor populations. It was also suggested that the emergence of the human quadrupedalism may be related to self-organizing processes occurring in complex systems, which select or attract one preferred behavioral state or locomotor trait out of many possible attractor states. Concerning the locomotor patterns, the dynamical systems in brain and body of the developing child may prefer some kind of locomotion, according to interactions of the internal components and the environmental conditions, without a direct role of any causative factor(s), such as genetic or neural codes, consistent with the concept of self-organization, suggesting no single element may have a causal priority

Evolvability signatures of generative encodings: beyond standard performance benchmarks

Evolutionary robotics is a promising approach to autonomously synthesize machines with abilities that resemble those of animals, but the field suffers from a lack of strong foundations. In particular, evolutionary systems are currently assessed solely by the fitness score their evolved artifacts can achieve for a specific task, whereas such fitness-based comparisons provide limited insights about how the same system would evaluate on different tasks, and its adaptive capabilities to respond to changes in fitness (e.g., from damages to the machine, or in new situations). To counter these limitations, we introduce the concept of "evolvability signatures", which picture the post-mutation statistical distribution of both behavior diversity (how different are the robot behaviors after a mutation?) and fitness values (how different is the fitness after a mutation?). We tested the relevance of this concept by evolving controllers for hexapod robot locomotion using five different genotype-to-phenotype mappings (direct encoding, generative encoding of open-loop and closed-loop central pattern generators, generative encoding of neural networks, and single-unit pattern generators (SUPG)). We observed a predictive relationship between the evolvability signature of each encoding and the number of generations required by hexapods to adapt from incurred damages. Our study also reveals that, across the five investigated encodings, the SUPG scheme achieved the best evolvability signature, and was always foremost in recovering an effective gait following robot damages. Overall, our evolvability signatures neatly complement existing task-performance benchmarks, and pave the way for stronger foundations for research in evolutionary robotics.Comment: 24 pages with 12 figures in the main text, and 4 supplementary figures. Accepted at Information Sciences journal (in press). Supplemental videos are available online at, see http://goo.gl/uyY1R

Robot Learning

The purpose of the project is to mimic human’s learning and motion mechanisms in order to create an adaptive walking gait on compliant humanoid robot - Atlas. The project applies neural controller theory based on Central Pattern Generators (CPG) to reduce a state (parameter) space from 100 states to an average of 10 states. The goal of the learning mechanism that utilizes unsupervised learning based on self-organizing maps and reward that adapts throughout the learning process is to find global optimal set of parameters for CPG. The learning mechanism also utilizes Covariance Matrix Adaptation – Evolutionary Strategies in order to converge to the parameter region that leads to stable walking gait (success region) quickly