Study On Dynamic Properties And Application Of Central Pattern Generator Model With Time Delay

The central pattern generator（CPG）plays an important role in the rhythmic movement of animals.CPG produces the rhythmic signal output to the animal muscle group,and controls its own rhythmic movement,thus produces various kinds of gait in the animal movement.its mathematical mechanism is the symmetrical coupling property of the oscillator which outputs the rhythmic signal,reacts on the model,and it is the multiple periodic solution of the symmetric dynamical system,and the change of animal gait is the interaction of the system modes.In this paper,we establish CPG time delay model withD₄ andZ₄×Z ₂lie symmetry for quadrupeds,and discuss the time-space symmetry breaking properties of these models,including stability,Hopf bifurcation,periodic solutions of multiple bifurcation,and so on.The key parameters of the CPG model are inversed and the method of gait cycle detection is given.The research is of great significance to the rhythmic motion and control of intelligent quadruped,and it can also provide theoretical support for the gait design of forestry robot.The main findings and results are as follows:（1）Based on the delay effect in signal transmission,the Van Der Pol（VDP）oscillator is used as the output signal oscillator of animal Central pattern generator.In this paper,a CPG neural network system consisting of four VDP oscillators（for short VDP-CPG neural network system）coupled with time delay is established.VDP-CPG neural network system is symmetrical with respect to dihedral group,therefore,the periodic solution of phase-locked vibration generated by the VDP-CPG neural network system corresponds to four simple gait systems of quadruped:walk gait,trot gait,pace gait and bound gait.In this paper,the existence conditions of equivariant Hopf bifurcation for a class of VDP symmetric systems are given with time delay as a parameter,by using the theory of symmetric bifurcation,the periodic solution of the space-time mode of the system and the bifurcation direction of the normal form and bifurcation periodic solution of the system on the center manifold are given by using trust region algorithm,the coupling strength parameters of delayed CPG neural networks constructed by VDP are inversed,and the representations of VDP-CPG neural networks for describing four basic gait patterns of quadrupeds are obtained,the range of coupling strength between vibrators of four gait systems is given,and the VDP-CPG model provides the theoretical basis for the basic gait design of forestry robot.（2）Based on the strong spatiotemporal symmetry of animal gait,aZ₄×Z ₂symmetric neural network system with time delay is established,and the conditions for generating equivariant bifurcation and the behaviors of bifurcation periodic solutions are obtained.Due to the dual symmetry of the system,a complex phase-locked vibration mode is generated,the corresponding bifurcating cycle solutions correspond to the six primary gait types of quadrupeds:walk,trot,pace,bound,pronk and jump.The system takes the time delay as the control parameter,and the system presents the rich phase-locked vibration pattern as the time delay varying.The results describe the transformation law of different gait in quadrupeds,and lay a theoretical foundation for the realization of gait transformation.The results of this study provide a theoretical basis for the primary gait design model of forestry robot,especially for the gait transformation design model.As an application combined with goat gait,this neural network model gives a gait design model of forestry robot based on goat gait by trust region inversion algorithm.（3）Gait cycle detection is an important step in the realization of vision-based gait recognition.In this paper,a class of convolutional neural network models are constructed.According to the characteristics of gait cycle,the gait sequence is classified and modeled.Taking the value of gait function corresponding to the CPG model constructed in the fourth chapter of this paper as a label,the gait cycle of quadrupeds can be detected by extracting the periodic features of gait frames using the convolutional neural network.The innovation of this paper is to establish two kinds of quadruped primary gait CPG models with time delay by using the equivariant bifurcation theory of symmetrical dynamic system,and give the space-time mode of bifurcation periodic solution of the model under the modal interaction in multi parameter space,which corresponds to six kinds of quadruped gait,so as to provide a theoretical basis for the gait generator and gait conversion model of bionic robot based on nonlinear vibrator.At the same time,a quadruped gait cycle detection method is given,which also lays a foundation for the research of gait planning of bionic robot.