By Mattia Frasca

ISBN-10: 9812389199

ISBN-13: 9789812389190

ISBN-10: 9812562303

ISBN-13: 9789812562302

This e-book offers with locomotion keep watch over of biologically encouraged robots learned via an analog circuital paradigm as mobile nonlinear networks. It provides a basic technique for the keep an eye on of bio-inspired robots and a number of other case experiences, in addition to describes a brand new method of movement regulate and the similar circuit architecture.Bio-inspired Emergent keep watch over of Locomotion platforms offers researchers with a advisor to the basics of the themes. in addition, neuro-biologists and physiologists can use the e-book as a kick off point to layout man made buildings for trying out their organic hypotheses at the animal version.

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Additional resources for Bio-inspired Emergent Control Of Locomotion Systems (World Scientific Series on Nonlinear Science, Series A, Vol. 48)

Example text

1) has an instable point (the origin when the biases are zeros; a point close to the origin otherwise) that is surrounded by a stable limit cycle for i2 < i,. Indeed no other fixed point exists in the phase plane x1 - x2 and since the flux is bounded, the hypotheses of the theorem are verified, thus proving the existence of the stable limit cycle. CNN-based CPGs with sensory feedback and VLSI implementation 45 When the bias i 2 is changed, other equilibria can arise. In this case the hypotheses of the Poincark-Bendixson theorem may no longer be valid.

8 Waveform 2 1 of system ( 3 . 1. ). it shows the period of oscillations versus the amplitude of the idealized ground contact signal. To match this plot with the 1 : 1 Arnold tongue shown in Fig. 7, the period of oscillations is on the x-axis, even if the period is a function of the applied signal amplitude. 9 allows us to draw the conclusion that the oscillations occur at the boundary of the 1 : 1 synchronization region. Therefore, this approach leads to a CPG able to show a locomotion pattern modulated by the sensory feedback, in which the stepping frequency is slower in absence of feedback.

1). This consideration and the PoincarBBendixson theorem allow us to draw conclusions on the global behavior of the system. When i2 > i, the limit cycle disappears and the trajectories go towards the stable equilibrium. 1 Near the bifurcation there is a bottleneck due to the “ghost” (or virtual) equilibrium point (see [Strogatz (1994)] and the discussion in Chap. 2). This leads to a slow-fast ratio in the system that depends on the value of the bias iz. 2 shows how the period T of oscillation depends on the parameter i2: the function T(i2) FZ (ic-::ll/3 (continuous line) is also shown for comparison; it has a similar form to that reported in [Strogatz (1994)].

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