Appendix 2

Abstract

The model of dynamics of a robot interacting with the environment is described by vector differential nonlinear equations of the form

$$H\left( q \right)\ddot q + h\left( {q,\dot q} \right) = \tau + J^T \left( q \right)F$$

((A.2.1))

where, q = q(t) is the n-dimensional vector of the robot generalized joint coordinates; H(q) is the n × n positive definite matrix of inertia moments of the manipulation mechanisms; h(q, q̇) is the n-dimensional nonlinear function of centrifugal, Coriolis’ and gravitational moments; τ = τ(t) is the n-dimensional vector of the input control; J ^T (q) is the n × m Jacobian matrix connecting velocities of the robot end-effector and velocities of the robot generalized coordinates; F = F(t) is the m-dimensional vector of the generalized forces or generalized forces and moments acting on the endeffector from the environment. Dimension of the vector F can be adopted in Cartesian coordinates to be 3 or 6. Presently, it will be assumed that n= m (generally n > m).