YAO Qijia, GE Xinsheng. Dynamics Modeling and Motion Planning for Snakeboard Systems Based on Differential Geometry[J]. Applied Mathematics and Mechanics, 2018, 39(1): 29-40. doi: 10.21656/1000-0887.380107
Citation: YAO Qijia, GE Xinsheng. Dynamics Modeling and Motion Planning for Snakeboard Systems Based on Differential Geometry[J]. Applied Mathematics and Mechanics, 2018, 39(1): 29-40. doi: 10.21656/1000-0887.380107

Dynamics Modeling and Motion Planning for Snakeboard Systems Based on Differential Geometry

doi: 10.21656/1000-0887.380107
Funds:  The National Natural Science Foundation of China(11472058)
  • Received Date: 2017-04-21
  • Rev Recd Date: 2017-05-23
  • Publish Date: 2018-01-15
  • Dynamics modeling and motion planning for snakeboard systems were investigated, and a hybrid optimization strategy based on the genetic algorithm (GA) and the Gauss pseudospectral method (GPM) was presented. Firstly, the Euler-Lagrange equations for the snakeboard system were derived based on the Riemannian manifold and the affine connection theory in differential geometry. The configuration space of the snakeboard corresponds to the manifold space, the velocity space corresponds to the tangent space, the torque space corresponds to the cotangent space, and the inertia matrix provides a Riemannian measure on the manifold. The set of admissible velocities were represented by the appropriate bases to simplify the kinematics equations. Then the optimal motion planning problem was transformed into a nonlinear programming problem with the GPM. The optimal trajectory and the optimal control inputs were obtained with the sequential quadratic programming (SQP) algorithm. The GA was applied to generate the initial values of the GPM. Finally, through numerical simulation, the optimal trajectory agrees well with actual conditions, and the control inputs match the various constraints closely. The results demonstrate the effectiveness of the proposed method.
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