Learnability and Adaptability from the Viewpoint of Passivity Analysis

Abstract

This paper attempts to give a mathematical and physical interpretation of practicebased learning (so-called 'learning control') from the passivity viewpoint for a class of linear dynamical systems with passivity and general nonlinear differential equations of robotic motion. It is shown from an axiomatic argument that the passivity of a pair of input and output plays a crucial role in the ability of learning. More precisely in case of robot dynamics it is shown that the passivity between a residual input torque vector and an output as a linear combination of the angular velocity error and the saturated joint angle error enables trajectory tracking errors of the robot motion to converge to zero with repeating practices. For a class of robot tasks when the endpoint is holonomically constrained on a surface, the problem of convergence of residual position and force trajectory tracking errors is also discussed under the joint-space orthogonalization principle.

Iterative Learning Control

“…Note that this approach does not change the result, because the triangular area included by points y 3 , y 6 , and y 10 does not add any value to vertex point values (i.e., y 10 and y 11 ) whereas if the maximum value still occurs at a vertex point after the triangular area is added, it is certain that the maximum value always occurs at a vertex point. Now, let us check the following: (4.8) which is rewritten as y = γ 1 1 x + γ 1 2 + y 1 + |γ 31 x + γ 32 |. Here, ignore y 1 , because y 1 is a constant value at all x (i.e., for all x ∈ [x, x]).…”

Modular stability tools for distributed computation and control

“…In this section we illustrate these properties with simple applications to modular design. An interesting recent discussion of the application of passivity tools to recursive refinement of the control of movement can be found in Reference [41].…”

On the Development of Learning Control for Robotic Manipulators

“…In [25], an iterative learning control that is formed on the basis of the passivity for 2-DOF robotic mechanisms with antagonistic bi-articular muscles is developed. The iterative learning control scheme is designed by resorting to the Arimoto-type iterative learning control presented in [26]. The closed-loop system's convergence is analyzed on the basis of passivity.…”