Novel analytical and experimental trajectory optimization of a 7-DOF baxter robot: global design sensitivity and step size analyses

High-order inverse dynamics is important for the trajectory tracking control of the elastic-joint manipulators. Usually it is undesirable to establish third-order or fourth-order inverse dynamics through the symbolic Lagrangian method, because of its complicated customization and higher computational complexity, which is not suitable for real-time control for multi-joint [Formula: see text] manipulators. Based on the Subsystem of Newton-Euler formulation and the recently proposed elastic joint Newton-Euler algorithm (EJNEA), a novel recursive algorithm (Sub-EJNEA) is proposed in this paper. The Sub-EJNEA obtains a linear complexity [Formula: see text], and has a more compact form and clear physical meaning. Based on the Sub-EJNEA, a recursive control method is proposed, which can be seen as an enhancement of the feedback linearization (FL-E) control method. When facing with friction and external disturbances, a combined controller FL-E-RISE is proposed. Finally, to verify the correctness of the recursive algorithm and the effectiveness of the proposed control schemes, simulation results with the Baxter manipulator are presented.

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“…The parameters of dynamics are listed in Table 1. [38][39][40] The joint stiffness and the drive inertia moments are set as follows:…”

Section: Simulation Resultsmentioning

confidence: 99%

A recursive inverse dynamics algorithm for robotic manipulators with elastic joints and its application to control

Xin

Chen

Gao

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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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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“…Also, MðqÞ 2 R 7Â7 ; Cðq; _ qÞ 2 R 7Â7 , and /ðqÞ 2 R 7 are the mass, Coriolis, and gravitational matrices, respectively. This coupled nonlinear dynamic model of the robot is used in the optimization process [43,44].…”

Section: Mathematical Modelingmentioning

confidence: 99%

Multivariable Extremum Seeking for Joint-Space Trajectory Optimization of a High-Degrees-of-Freedom Robot

Bagheri

Krstić

2018

Journal of Dynamic Systems, Measurement, and Control

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In this paper, a novel analytical coupled trajectory optimization of a seven degrees-of-freedom (7DOF) Baxter manipulator utilizing extremum seeking (ES) approach is presented. The robotic manipulators are used in network-based industrial units, and even homes, by expending a significant lumped amount of energy, and therefore, optimal trajectories need to be generated to address efficiency issues. These robots are typically operated for thousands of cycles resulting in a considerable cost of operation. First, coupled dynamic equations are derived using the Lagrangian method and experimentally validated to examine the accuracy of the model. Then, global design sensitivity analysis is performed to investigate the effects of changes of optimization variables on the cost function leading to select the most effective ones. We examine a discrete-time multivariable gradient-based ES scheme enforcing operational time and torque saturation constraints in order to minimize the lumped amount of energy consumed in a path given; therefore, time-energy optimization would not be the immediate focus of this research effort. The results are compared with those of a global heuristic genetic algorithm (GA) to discuss the locality/globality of optimal solutions. Finally, the optimal trajectory is experimentally implemented to be thoroughly compared with the inefficient one. The results reveal that the proposed scheme yields the minimum energy consumption in addition to overcoming the robot's jerky motion observed in an inefficient path.

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Novel analytical and experimental trajectory optimization of a 7-DOF baxter robot: global design sensitivity and step size analyses

Cited by 11 publications

References 51 publications

A recursive inverse dynamics algorithm for robotic manipulators with elastic joints and its application to control

A recursive inverse dynamics algorithm for robotic manipulators with elastic joints and its application to control

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

Multivariable Extremum Seeking for Joint-Space Trajectory Optimization of a High-Degrees-of-Freedom Robot

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