Serpentine and Rectilinear Motion Generation in Snake Robot Using Central Pattern Generator with Gait Transition

Abstract

This paper contributes to the fabrication of a snake-like robot in which the motion can be achieved through active wheels. The robot is constructed in such a way that its size can be increased and decreased, as well as it can undulate into a sine wave-like shape. The snake robot with wheels consists of chain of links attached to each other with the help of the passive prismatic and revolute joints. A neural oscillator-based central pattern generator (CPG) algorithm is applied to the robot so that rhythmic serpentine as well as rectilinear motions can be generated in it. In addition, a novel smooth transition mechanics of robot motion, from stationary position to serpentine or rectilinear motion as well as transition between these two gaits, is also suggested in the paper. The working of the formulated CPG motion algorithm is realized through experimental setup equipped with a motion capture system as well as through simulations.

Appendix: Phase Difference

• 1. The phase difference $\varPhi _{j,k}$ in the serpentine motion is selected so that the desired orientation of the wheel-links should be sinusoidal and the length of each prismatic joint remain constant. This would generate continuous, nonnegative, sinusoidal neuron firing. To achieve these requirements, the coupled neurons of the same wheel-link and prismatic joint are taken out of phase (e.g., $\varPhi _{j,k}=\pm \pi$);

  $$\begin{aligned} \varPhi _{j,k}=\pm \pi \quad \forall \quad j=k \end{aligned}$$

  (21)

  While the phase difference between the neurons of adjacent wheel-links are set such that

  $$\begin{aligned} \varPhi _{j,k}=\pm \frac{2n\pi }{m}\quad \forall \quad j\ne k \end{aligned}$$

  (22)

  where n is the total number of required sine waves for robot. Thus, the phase difference between the neurons of adjacent wheel-links should be equal to $\varPhi _{j,k}= \pm \frac{2\pi }{m}$ for one full sine wave.

• 2. In the rectilinear locomotion, the orientation of all the wheels should be same, along the horizontal direction of snake coordinate. The length of the prismatic joints should alternatively change from tail to head (wheel-links should move alternatively). This can be achieved such that the neuron of same coupled oscillators should fire simultaneously, i.e., $\varPhi _{j,k}= 0$.

  $$\begin{aligned} \varPhi _{j,k}=\pm 0 \quad \forall \quad j=k \end{aligned}$$

  (23)

  Along with phase differences between neurons of the adjacent wheel-links are taken such that

  $$\begin{aligned} \varPhi _{j,k}=\pm \frac{2\pi }{m}\quad \forall \quad j\ne k \end{aligned}$$

  (24)

  in this way total sum of all phase difference becomes $2\pi$.