ABSTRACT
This chapter illustrates and analyzes the application of adaptive PID to robotic
systems. Detail design, analysis and simulation are provided.
Consider an n-joint rigid-link robotic manipulator with the following joint-space
dynamics
Dq(q)q¨+Cq(q, q˙)q˙+Gq(q)+ τ(q˙, t) = ua (9.1)
where q ∈ Rn is the joint displacement; D(q) ∈ Rn×n, Cq(q, q˙) ∈ Rn×n and Gq(q) ∈ Rn are the symmetric positive definite inertial matrix, Coriolis and centrifugal matrix, and gravitational force vector, respectively; τ(q˙, t) ∈ Rn represents the non-parametric frictional and the modeling uncertainties; ua ∈ Rn denotes the control vector of joint torque/force. Then for different tasks, we need to
deal with different type of systems (i.e., square or non-square systems).
