Joint-Space Trajectory Optimization of a 7-DOF Baxter Using Multivariable Extremum Seeking

Bagheri, Mostafa; Krstić, Miroslav

doi:10.23919/acc.2018.8430959

Cited by 6 publications

(1 citation statement)

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“…The robot manipulator is modeled as followswhere q , q˙, and trueq¨∈ℝ7 are angles, angular velocities, and accelerations of joints, respectively, and τ∈ℝ7 indicates the vector of joints’ driving torques. Also, M ( q ) ∈ R 7×7 , C(q,trueq˙)∈R7×7, and ϕ(q)∈ℝ7 are the mass, Coriolis, and gravitational matrices, respectively, which are symbolically derived using the Euler–Lagrange equation Bagheri et al (2019a, 2019b), Bagheri et al (2018b, 2017), Bagheri (2019), Bagheri et al (2018c), Bertino et al (2019), Bagheri et al (2019a, 2019b), Bagheri et al (2018a), Bagheri and Naseradinmousavi (2017), Bagheri et al (2021). The inertia matrix M ( q ) is symmetric, positive definite, and consequently invertible.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Analytical and experimental nonzero-sum differential game-based control of a 7-DOF robotic manipulator

Bagheri¹

2021

Journal of Vibration and Control

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We formulate a Nash-based feedback control law for an Euler–Lagrange system to yield a solution to noncooperative differential game. The robot manipulators are broadly used in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler–Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability.

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