Caterpillar crawling is distinct from that of other limbless animals. It is simple but efficient. This paper presents a novel mechanism to duplicate the movement to a modular caterpillar-like robot. First, how caterpi...Caterpillar crawling is distinct from that of other limbless animals. It is simple but efficient. This paper presents a novel mechanism to duplicate the movement to a modular caterpillar-like robot. First, how caterpillars move in nature is investigated and analyzed systematically. Two key locomotive properties are abstracted from the body shape of caterpillars during crawling. Then, based on a morphological mapping, a hypothesis of asymmetric oscillation with a ratio of two is proposed, followed by a thorough analysis of the kinematics of the caterpillar-like robot. The asymmetric oscillating mechanism is proved capable of generating stable caterpillar-like locomotion. Next, taking advantage of the two locomotive properties and the hypothesis, a new Central Pattern Generator （CPG） model is designed as the controller of the robot. The model can not only generate the signal as expected, but also provide explicit control parameters for online modulation. Finally, simulation and on-site experiments are carried out. The results confirm that the proposed method is effective for caterpillar-like locomotion.展开更多
We establish the coexistence of periodic solution and unbounded solution, the infinity of largeamplitude subharmonics for asymmetric weakly nonlinear oscillator x' + a2x+ - b2x- + h(x) = p(t) with h(±∞) - 0 ...We establish the coexistence of periodic solution and unbounded solution, the infinity of largeamplitude subharmonics for asymmetric weakly nonlinear oscillator x' + a2x+ - b2x- + h(x) = p(t) with h(±∞) - 0 and xh(x) → +∞(x →∞), assuming that M(τ ) has zeros which are all simple and M(τ ) 0respectively, where M(τ ) is a function related to the piecewise linear equation x' + a2x+ - b2x- = p(t).展开更多
In this paper,we prove the existence of quasi-periodic solutions and the boundedness of all the solutions of the general semilinear quasi-periodic differential equation x′′+ax^(+)-bx^(-)=G_x(x,t)+f (t),where x^(+)=m...In this paper,we prove the existence of quasi-periodic solutions and the boundedness of all the solutions of the general semilinear quasi-periodic differential equation x′′+ax^(+)-bx^(-)=G_x(x,t)+f (t),where x^(+)=max{x,0},x^(-)=max{-x,0},a and b are two different positive constants,f(t) is C^(39) smooth in t,G(x,t)is C^(35) smooth in x and t,f (t) and G(x,t) are quasi-periodic in t with the Diophantine frequency ω=(ω_(1),ω_(2)),and D_(x)^(i)D_(t)^(j)G(x,t) is bounded for 0≤i+j≤35.展开更多
文摘Caterpillar crawling is distinct from that of other limbless animals. It is simple but efficient. This paper presents a novel mechanism to duplicate the movement to a modular caterpillar-like robot. First, how caterpillars move in nature is investigated and analyzed systematically. Two key locomotive properties are abstracted from the body shape of caterpillars during crawling. Then, based on a morphological mapping, a hypothesis of asymmetric oscillation with a ratio of two is proposed, followed by a thorough analysis of the kinematics of the caterpillar-like robot. The asymmetric oscillating mechanism is proved capable of generating stable caterpillar-like locomotion. Next, taking advantage of the two locomotive properties and the hypothesis, a new Central Pattern Generator （CPG） model is designed as the controller of the robot. The model can not only generate the signal as expected, but also provide explicit control parameters for online modulation. Finally, simulation and on-site experiments are carried out. The results confirm that the proposed method is effective for caterpillar-like locomotion.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10071055).
文摘We establish the coexistence of periodic solution and unbounded solution, the infinity of largeamplitude subharmonics for asymmetric weakly nonlinear oscillator x' + a2x+ - b2x- + h(x) = p(t) with h(±∞) - 0 and xh(x) → +∞(x →∞), assuming that M(τ ) has zeros which are all simple and M(τ ) 0respectively, where M(τ ) is a function related to the piecewise linear equation x' + a2x+ - b2x- = p(t).
基金supported by National Natural Science Foundation of China (Grant No.11571327)。
文摘In this paper,we prove the existence of quasi-periodic solutions and the boundedness of all the solutions of the general semilinear quasi-periodic differential equation x′′+ax^(+)-bx^(-)=G_x(x,t)+f (t),where x^(+)=max{x,0},x^(-)=max{-x,0},a and b are two different positive constants,f(t) is C^(39) smooth in t,G(x,t)is C^(35) smooth in x and t,f (t) and G(x,t) are quasi-periodic in t with the Diophantine frequency ω=(ω_(1),ω_(2)),and D_(x)^(i)D_(t)^(j)G(x,t) is bounded for 0≤i+j≤35.
