基于微分几何的蛇形机器人移动与操作统一动力学模型研究

A unified dynamic model for locomotion and manipulation of a snake-like robot based on differentialgeometry

蛇形机器人本体是一种多关节串联机构,可以在各种环境中运动,并且当一端固定时可以实现操作.本文提出一种蛇形机器人移动与操作的统一动力学建模方法,统一蛇形机器人移动状态及操作状态的动力学方程.机器人从移动状态到操作状态的转换意味着机构上的重构,即移动状态无固定基座,而操作状态有固定基座.应用虚设机构法在机构学上统一这两种状态(即构形空间中的嵌入关系),利用指数积公式描述这两种状态的运动学方程.在Riemann流形上建立起蛇形机器人移动和操作的动力学模型,并在对动力学模型中各项计算分析的基础上发现机器人操作动力学方程可直接由移动动力学方程退化得到,同时应用子流形的Gauss公式给出证明.由此在微分几何框架下建立蛇形机器人移动与操作的统一动力学模型.按照几何的观点将蛇形机器人移动与操作动力学模型的统一看作是子流形问题,并赋予几何意义.较单独针对蛇形机器人的一种状态(移动或操作)的动力学模型而言,这种统一的动力学模型能够更深刻地揭示蛇形机器人动力学的特征.

A snake-like robot,whose body is a seried-wound articulated mechanism,can move in various environments.In addition,when one end is fixed on a base,the robot can manipulate objects.A method of dynamic modeling for locomotion and manipulation of the snake-like robot is developed in order to unify the dynamic equations of two states.The transformation from locomotion to manipulation is a mechanism reconfiguration,that is,the robot in locomotion has not a fixed base,but it in manipulation has one.First,a virtual structure method unifies the two states in mechanism（e.g.,an embedding in the configuration space）;second,the product-of-exponentials formula describes the kinematics;third,the dynamics of locomotion and manipulation are established in a Riemannian manifold;finally,based on the analysis of the dynamic model,the dynamics of manipulation can be directly degenerated from those of locomotion,and this degeneration relation is proved through using the Gauss equations.In the differential geometry formulation,this method realizes the unification of the dynamics of locomotion and manipulation.According to a geometrical point of view,the unified dynamic model for locomotion and manipulation is considered as a submanifold problem endowed with geometric meaning.In addition,the unified model offers an insight into the dynamics of the snake-like robot beyond the dynamic model separately established for locomotion or manipulation.