Trajectory Tracking of a One-Link Flexible Arm via Iterative Learning Control

Abstract

Trajectory tracking of flexible link robots is a classical control problem. Historically, the link elasticity was considered as something to be removed. Hence, the control performance was guaranteed by adopting high-gain feedback loops and, possibly, a dynamic compensation with the result to stiffen up the dynamic behavior of the robot. Nowadays, robots are pushed more and more towards a safe physical interaction with a less and less structured environment. Hence, the design and control of the robots moved to an on-purpose introduction of highly compliant elements in the robot bodies, the so-called soft robotics, and towards control approaches that aim to provide the tracking performance without a substantial change in the robot dynamic behavior. Following this approach, we present an iterative learning control that relies mainly on a feedforward component, hence preserves the robot dynamics, for trajectory tracking of a one-link flexible arm. We provide a condition, based on the system dynamics and similar to the Strong Inertially Coupled property, that ensures the applicability of the proposed control method. Finally, we report simulation and experimental tests to validate the theoretical results.

A Robust Iterative Learning Control for Continuous-Time Nonlinear Systems With Disturbances

“…In this paper we employ an ILC control law, which is purely feedforward. This has already been widely used in literature, for example in [9] and [30], achieving G1). Recalling the system (1)-( 2) and the assumptions A1)-A5), we employed control law is…”

“…. , r are tunable control gain matrices, which affect the convergence velocity [9]. The initial guess u 0 (t) ∈ R m of the iterative control law (3) can be arbitrarily chosen.…”

“…We simulate the dynamics of a two DoFs underactuated arm with elastic joints. We refer to [9] for a more exhaustive treatment of the system dynamics. Let = 0.55 kg, J = 0.001 kgm 2 , l = 0.085 m, a = 0.089 m, and d ν = 0.3 Nms/rad be the mass, inertia, length, center of mass distance, and damping of each link, respectively.…”

“…Additionally, we test the control algorithm simulating measurement noise d rty j (t), external disturbances, and delays in the controller u j (t), which can be both modeled as state-nonrepetitive disturbances d rx j (x j (t)) in (1). The chosen output function h(x) ∈ R is the absolute angle of the robot tip i.e., y = x 1 + x 2 , which leads to a relative degree r = 2 iff ( [9])…”

PIσ - PIσ Continuous Iterative Learning Control for Nonlinear Systems with Arbitrary Relative Degree

“…An alternative solution based on sample data update law is proposed in [10]. A learning rule for an underactuated robot with relative degree two is proposed and experimentally validated in [11].…”