Fractional central pattern generators for bipedal locomotion

Locomotion has been a major research issue in the last few years. Many models for the locomotion rhythms of quadrupeds, hexapods, bipeds and other animals have been proposed. This study has also been extended to the control of rhythmic movements of adaptive legged robots. In this paper, we consider a fractional version of a central pattern generator (CPG) model for locomotion in bipeds. A fractional derivative D α f(x), with α non-integer, is a generalization of the concept of an integer derivative, where α=1. The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a network of four coupled identical oscillators which has dihedral symmetry. We study parameter regions where periodic solutions, identified with legs’ rhythms in bipeds, occur, for 0<α≤1. We find that the amplitude and the period of the periodic solutions, identified with biped rhythms, increase as α varies from near 0 to values close to unity

Towards a neural hierarchy of time scales for motor control

Animals show remarkable rich motion skills which are still far from realizable with robots. Inspired by the neural circuits which generate rhythmic motion patterns in the spinal cord of all vertebrates, one main research direction points towards the use of central pattern generators in robots. On of the key advantages of this, is that the dimensionality of the control problem is reduced. In this work we investigate this further by introducing a multi-timescale control hierarchy with at its core a hierarchy of recurrent neural networks. By means of some robot experiments, we demonstrate that this hierarchy can embed any rhythmic motor signal by imitation learning. Furthermore, the proposed hierarchy allows the tracking of several high level motion properties (e.g.: amplitude and offset), which are usually observed at a slower rate than the generated motion. Although these experiments are preliminary, the results are promising and have the potential to open the door for rich motor skills and advanced control

Adaptive, fast walking in a biped robot under neuronal control and learning

Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (&gt; 3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks

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

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