Model identification for robot manipulators using regressor-free adaptive control

Abstract

This paper proposes a regressor-free adaptive feedback-linearization control technique that does not require a model approximation or a regressor matrix. Adaptation in the proposed feedback process is acquired through an update law involving adjustment of less control parameters as compared to existing controllers. Under the given constraints, the closed-loop asymptotic stability of the proposed control law is verified using Lyapunov techniques. The proposed controller is compared with existing adaptive controllers on a two degree-of-freedom robot manipulator. Based on the new adaptive technique, the model parameters of the robotic arm are identified using adequate excitation trajectories. The proposed adaptive technique was validated through simulations and experiments.

Addressing Control Implementation Issues in Robotic Systems Using Adaptive Control

“…With ease of implementation in mind, we introduce a first-order version of a robust-adaptive controller introduced in our previous work. 3,4 An advantage of the first-order controller is the use of few control parameters compared to the higher-order adaptive control. In Section 3, rigorous stability and robustness proofs are performed for the first-order adaptive controller.…”

“…By considering a high value for the controller gain 'a', the mismatch will vanish quickly. 3 Once the vectorφ → φ, the outer loop will achieve the desired specification by tuning the PD gains K d and K p .…”

“…M(1, 1) 1.04 + 0.08cos(q 2 + q 3 ) + 0.34cos(q 2 ) + 0.05cos(q 3 ) M (1,2) 0.43 + 0.04cos(q 2 + q 3 ) + 0.17cos(q 2 ) + 0.05cos(q 3 ) = M(2, 1) M (1,3) 0.17 + 0.04cos(q 2 + q 3 ) + 0.023cos(q 3 ) = M(3, 1) M (2,2) 0.43 + 0.05cos(q 3 ) M (2,3) 0.17 shows that the error at steady state is much lower than 0.01 rad/s for all time during steady state. For one complete rotation of the end effector, the desired trajectory requires 3.14 s. Here the assumption is that the torque requirements for the desired trajectory are lower than the saturation.…”

Incremental Model Predictive Control Exploiting Time-Delay Estimation for a Robot Manipulator

“…k|k −x 2,k−1|k /T s = ẋ2 (k) + ω 2 (k). (41)Replacing ẋ2 (k) in (40) by(41) yieldsu(k) = g −1 (x(k)) x 2,k|k −x 2,k−1|k /T s −ω 2 (k)−f (x(k)) . (42) According to Property 1 and Assumption 1, one has∥u(k)∥ ≤ µ 2 (∥K 1 X(k)∥+ω 2,max +f max ∥x(k)∥+f 0 ) (43)In accordance with Assumption 2, it is obtained that∥K 1 X(k)∥ ≤ ∥K 1 ∥ (∥E(k)∥+∥X ref (k)∥) ≤ k 1 (∥E(k)∥+r b1 ) ,(44) ∥x(k)∥ ≤ ∥e(k)∥ + ∥x ref (k)∥ ≤ ∥E(k)∥ + r b2 .…”