基于微分几何的蛇形机器人动力学与控制统一模型

Abstract

Whereas the inputs for a snakelike robot are torques, the dynamics system is a nonlinear control system. With increasing modules in a snakelike robot, its nonlinear control system becomes complex and inconvenient for regulation and control. In this paper, the differential geometry method is used, and the Euler-Lagrange equations are extended to equations under any base. Thus, the dynamics equations are reduced to the standard affine control system, and the dynamics-control unified model is derived; this simplifies the regulation and control of the snakelike robot. Based on the unified model, a partial feedback linearization method is developed, and the head trajectory controller is designed. The configuration space of a snakelike robot corresponds to the manifold space, the velocity corresponds to the tangent space, the torque space corresponds to the cotangent space, and the kinematic energy provides a Riemann measure on the manifold. Thus, the dynamics of a snakelike robot can be described by Riemann geometry. Additionally, the passive wheels installed under the snakelike robot introduce the velocity constraint, which constrains the velocity space to a subspace of the tangent space. That is, the velocity space forms a distribution, and the dynamics system becomes a nonholonomic dynamics system. For a snakelike robot with passive wheels, the configuration is a Riemann manifold with a distribution. In the distribution, the appropriate base can be chosen to simplify the dynamics. In this paper, a base model is built based on the fiber bundle theory. Any set base is only a section in the fiber bundle. The orthogonal normalization technique is adopted to derive a set base that can simplify the dynamics calculation, and the dynamics-control unified model is derived. Finally, a nine-module snakelike robot is used as an example of the partial feedback linearization method.