Hexapod locomotion : a nonlinear dynamical systems approach

The ability of walking in a wide variety of terrains is one of the most important features of hexapod insects. In this paper we describe a bio-inspired controller able to generate locomotion and switch between different type of gaits for an hexapod robot. Motor patterns are generated by coupled Central Pattern Generators formulated as nonlinear oscillators. These patterns are modulated by a drive signal, proportionally changing the oscillators frequency, amplitude and the coupling parameters among the oscillators. Locomotion initiation, stopping and smooth gait switching is achieved by changing the drive signal. We also demonstrate a posture controller for hexapod robots using the dynamical systems approach. Results from simulation using a model of the Chiara hexapod robot demonstrate the capability of the controller both to locomotion generation and smooth gait transition. The postural controller is also tested in different situations in which the hexapod robot is expected to maintain balance. The presented results prove its reliability

Gait generation for a simulated hexapod robot : a nonlinear dynamical systems approach

The capacity of walking in a wide variety of terrains is one of the most important features of hexapod insects. In this paper we describe a bio-inspired controller able to generate locomotion and reproduce the different type of gaits for an hexapod robot. Motor patterns are generated by coupled Central Pattern Generators, formulated as nonlinear oscillators. In order to demonstrate the robustness of the controller we developed a simulation model of the real Chiara hexapod robot where are described the most important steps of its development. Results were performed in simulation using the developed model of the Chiara hexapod robot

A new CPG model for the generation of modular trajectories for hexapod robots

Legged robots are often used in a large variety of tasks, in different environments. Nevertheless, due to the large number of degrees-of-freedom to be controlled, online generation of trajectories in these robots is very complex. In this paper, we consider a modular approach to online generation of trajectories, based on biological concepts, namely Central Pattern Generators (CPGs). We introduce a new CPG model for hexapod robots’ rhythms, based in the work of Golubitsky et al (1998). Each neuron/oscillator in the CPG consists of two modules/primitives: rhythmic and discrete. We study the effect on the robots’ gaits of superimposing the two motor primitives, considering two distinct types of coupling.We conclude, from the simulation results, that the amplitude and frequency of periodic solutions, identified with hexapods’ tripod and metachronal gaits, remain constant for the two couplings, after insertion of the discrete part.CP was supported by Research funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT Fundacao para a Ciencia e a Tecnologia under the project PEst-C/MAT/UI0144/2011. This work was also funded by FEDER Funding supported by the Operational Program Competitive Factors COMPETE and National Funding supported by the FCT - Portuguese Science Foundation through project PTDC/EEACRO/100655/2008

A modular approach for trajectory generation in biped robots

Robot locomotion has been a major research issue in the last decades. In particular, humanoid robotics has had a major breakthrough. The motivation for this study is that bipedal locomotion is superior to wheeled approaches on real terrain and situations where robots accompany or replace humans. Some examples are, on the development of human assisting device, such as prosthetics, orthotics, and devices for rehabilitation, rescue of wounded troops, help at the office, help as maidens, accompany and assist elderly people, amongst others. Generating trajectories online for these robots is a hard process, that includes different types of movements, i.e., distinct motor primitives. In this paper, we consider two motor primitives: rhythmic and discrete.We study the effect on a bipeds robots’ gaits of inserting the discrete part as an offset of the rhythmic primitive, in synaptic and diffusive couplings. Numerical results show that amplitude and frequency of the periodic solution, corresponding to the gait run are almost constant in all cases studied here.(undefined

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

Three People Can Synchronize as Coupled Oscillators during Sports Activities

We experimentally investigated the synchronized patterns of three people during sports activities and found that the activity corresponded to spatiotemporal patterns in rings of coupled biological oscillators derived from symmetric Hopf bifurcation theory, which is based on group theory. This theory can provide catalogs of possible generic spatiotemporal patterns irrespective of their internal models. Instead, they are simply based on the geometrical symmetries of the systems. We predicted the synchronization patterns of rings of three coupled oscillators as trajectories on the phase plane. The interactions among three people during a 3 vs. 1 ball possession task were plotted on the phase plane. We then demonstrated that two patterns conformed to two of the three patterns predicted by the theory. One of these patterns was a rotation pattern (R) in which phase differences between adjacent oscillators were almost 2π/3. The other was a partial anti-phase pattern (PA) in which the two oscillators were anti-phase and the third oscillator frequency was dead. These results suggested that symmetric Hopf bifurcation theory could be used to understand synchronization phenomena among three people who communicate via perceptual information, not just physically connected systems such as slime molds, chemical reactions, and animal gaits. In addition, the skill level in human synchronization may play the role of the bifurcation parameter

Bipedal Locomotion: A Fractional CPG for Generating Patterns

Proceedings of the 10th Conference on Dynamical Systems Theory and ApplicationsThere has been an increase interest in the study of animal locomotion. Many models for the generation of locomotion patterns of different animals, such as centipedes, millipedes, quadrupeds, hexapods, bipeds, have been proposed. The main goal is the understanding of the neural bases that are behind animal locomotion. In vertebrates, goal-directed locomotion is a complex task, involving the central pattern generators located somewhere in the spinal cord, the brainstem command systems for locomotion, the control systems for steering and control of body orientation, and the neural structures responsible for the selection of motor primitives. In this paper, we focus in the neural networks that send signals to the muscle groups in each joint, the so-called central pattern generators (CPGs). We consider a fractional version of a CPG model for locomotion in bipeds. A fractional derivative) Dα 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 four cells model, where each cell is modelled by a system of ordinary differential equations. The coupling between the cells allows two independent permutations, and, as so, the system has D2 symmetry. We consider 0 < α ≤ 1 and we compute, for each value of α, the amplitude and the period of the periodic solutions identified with two legs' patterns in bipeds. We find the amplitude and the period increase as α varies from zero up to one