Controllability and Stability Analysis of Planar Snake Robot Locomotion

Dept. of Eng. Cybern., Norwegian Univ. of Sci. & Technol. (NTNU), Trondheim, Norway
IEEE Transactions on Automatic Control (Impact Factor: 2.78). 07/2011; 56(6):1365 - 1380. DOI: 10.1109/TAC.2010.2088830
Source: IEEE Xplore


This paper contributes to the understanding of snake robot locomotion by employing nonlinear system analysis tools for investigating fundamental properties of snake robot dynamics. The paper has five contributions: 1) a partially feedback linearized model of a planar snake robot influenced by viscous ground friction is developed. 2) A stabilizability analysis is presented proving that any asymptotically stabilizing control law for a planar snake robot to an equilibrium point must be time-varying. 3) A controllability analysis is presented proving that planar snake robots are not controllable when the viscous ground friction is isotropic, but that a snake robot becomes strongly accessible when the viscous ground friction is anisotropic. The analysis also shows that the snake robot does not satisfy sufficient conditions for small-time local controllability (STLC). 4) An analysis of snake locomotion is presented that easily explains how anisotropic viscous ground friction enables snake robots to locomote forward on a planar surface. The explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion. 5) A controller for straight line path following control of snake robots is proposed and a Poincaré map is investigated to prove that the resulting state variables of the snake robot, except for the position in the forward direction, trace out an exponentially stable periodic orbit.

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Available from: Pål Liljebäck, May 09, 2015
    • "A drawback of [19] is that the stability analysis is valid for a simplified model that is valid only for small joint angles. Another drawback of [18] and [19] is that they are only valid for straight lines and not all curved paths. To the best of our knowledge, to date, there is no proof of convergence of a path-following controller for the complete nonlinear model of a holonomic snake robot. "
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    ABSTRACT: This paper investigates the problem of maneuvering control for planar snake robots. The control objective is to make the center of mass of the snake robot converge to a desired path and traverse the path with a desired velocity. The proposed feedback control strategy enforces virtual constraints encoding a lateral undulatory gait, parametrized by the states of dynamic compensators used to regulate the orientation and forward speed of the snake robot.
    No preview · Article · Aug 2015 · IEEE Transactions on Control Systems Technology
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    • "The method of Poincaré maps is a widely used tool for studying the stability of periodic solutions in dynamical systems. Poincaré maps are employed in [2], [21] to study the stability properties of ground snake robot locomotion. "
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    ABSTRACT: This paper considers straight line path following control of underwater snake robots in the presence of constant irrotational currents. An integral line-of-sight (LOS) guidance law is proposed, which is combined with a sinusoidal gait pattern and a directional controller that steers the robot towards and along the desired path. Integral action is introduced in the guidance law to compensate for the ocean current effect. The stability of the proposed control scheme in the presence of ocean currents is investigated. In particular, using Poincaré map analysis, we prove that the state variables of an underwater snake robot trace out an exponentially stable periodic orbit when the integral LOS path following controller is applied. Simulation results are presented to illustrate the performance of the proposed path following controller for both lateral undulation and eel-like motion.
    Full-text · Conference Paper · Dec 2014
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    • "터를 다음과 같이 sinq=[sinq 1 , sinq 2 , sinq 3 , sinq 4 ] T , Sinq=diag(sinq), cosq=[cosq 1 , cosq 2 , cosq 3 , cosq 4 ] T , Cosq=diag(cosq)으로 정의하였 다. 또한 그림 3(a)에서 상대 각도 j i = q i+1 – q i 로 정의하였다. 그림 3(a)에서 각 링크는 x, y 방향으로 식 (1), (2)와 같은 제한 조건을 가지고 있다[11] [12] "
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    ABSTRACT: Mammals such as dogs and cheetahs change their gait from trot to gallop as they run faster. However, lizards always trot for various speeds of running. When mammals run slowly with trot gait, their fore leg and hind leg generate the required force for acceleration or deceleration such that the yaw moments created by these forces cancel each other. On the other hand, when lizards run slowly, their fore legs and hind legs generate the forces for deceleration and acceleration, respectively. In this paper, the yaw motion of a lizard model is controlled by the movement of their waist and tail, and the reaction moment from the ground produced by the hind legs in simulation. The simulation uses the whole body dynamics of a lizard model, which consists of 4 links based on the Callisaurus draconoides. The results show that the simulated trotting of the model is similar to that of a real lizard when the movement of the model is optimized to minimize the reaction moment from the ground. It means that the body of a lizard moves in such a way that the reaction moment from the ground is minimized. This demonstrates our hypothesis on how lizards trot using body motion.
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