tailieunhanh - Adaptive Motion of Animals and Machines - Hiroshi Kimura et al (Eds) part 10

Tham khảo tài liệu 'adaptive motion of animals and machines - hiroshi kimura et al (eds) part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 180 Auke Jan Ijspeert and Jean-Marie Cabelguen 4 Locomotion controller Nonlinear oscillator We construct our models of the CPGs by using the following nonlinear oscillator to represent a local oscillatory center TV -a X V - E V - x E TX V where T a and E are positive constants. This oscillator has the interesting property that its limit cycle behavior is a sinusoidal signal with amplitude vE and period 2nT x t indeed converges to X t ỵ Esin t T ỷ where Ộ depends on the initial conditions see also Figure 2 right . We assume that the different oscillators of the CPG are coupled together by projecting to each other signals proportional to their X and V states in the following manner TVi - a i v Vi Xi y aij Xj bij Vj Cij Sj Ei jj TXi Vị where aij and bij are constants positive or negative determining how oscillator j influences oscillator i. In these equations the influence from sensory inputs Sj weighted by a constant cij is also added see next sections for further explanations. Body CPG We assume that the body CPG is composed of a double chain of oscillators all along the 40 segments of spinal cord. The type of connections investigated in this article are illustrated in Figure 3 left . For simplicity we assume that only nearest neighbor connections exist between oscillators. In our first investigation the oscillators are assumed to be identical along the chain with identical projections as well as between each side of the body. The connectivity of the chain is therefore defined by 6 parameters two the aij and bij parameters for each projection from one oscillator to the other . the rostral caudal and contralateral projections . Of these 6 parameters we fixed the couplings between contralateral oscillators to aij 0 and bij in order to force them to oscillate in anti-phase. We systematically investigated the different combinations of the four remaining parameters the rostral and caudal projections with values ranging from to with a step. .