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

Abstract

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.

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

“…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.…”

An adaptive and energy-maximizing control of wave energy converters using extremum-seeking approach

“…The objective here is to optimize m parameters simultaneously. For stability analysis of ES control of SISO system, we refer the readers to Krstić and Wang [7], and of MISO system, the readers are referred to [33,34,35,36,37,11,12].…”

“…ES is an adaptive control which tracks a maximum/minimum (extremum) of a performance/cost function and then drives the output of this function to its extremum [7]. ES control has been used for a variety of applications, including but not limited to, reducing thermo-acoustic instabilities in gas turbines and rocket engines [8], flight formation optimization [9], control of thermo-acoustic coolers [10], autonomous vehicles [11], and robots [12], and beam matching in particle accelerators [13]. ES control has also been widely used for wind [14,15,16], and solar power applications [17,18,19].…”

An Angle Error Compensation Method Based on Harmonic Analysis for Integrated Joint Modules

“…Trajectory planning considers obstacle avoidance, time optimization and motion stability. Early literature has used the maximum speed or acceleration constraints to select the optimal speed or acceleration curve for determining the path and trajectory [2], the maximum principle to solve the time optimal trajectory planning [3] and various optimal algorithms of nonlinear constraint [4] and has even introduced intelligent algorithms such as neural networks, genetic algorithms or other algorithms for time optimal trajectory planning [5][6][7]. In terms of accuracy control, manipulator error can be caused by many influencing factors, further complicating the problem of error compensation.…”