Discovering Stick-Slip-Resistant Servo Control Algorithm Using Genetic Programming

Abstract

The stick-slip is one of negative phenomena caused by friction in servo systems. It is a consequence of complicated nonlinear friction characteristics, especially the so-called Stribeck effect. Much research has been done on control algorithms suppressing the stick-slip, but no simple solution has been found. In this work, a new approach is proposed based on genetic programming. The genetic programming is a machine learning technique constructing symbolic representation of programs or expressions by evolutionary process. In this way, the servo control algorithm optimally suppressing the stick-slip is discovered. The GP training is conducted on a simulated servo system, as the experiments would last too long in real-time. The feedback for the control algorithm is based on the sensors of position, velocity and acceleration. Variants with full and reduced sensor sets are considered. Ideal and quantized position measurements are also analyzed. The results reveal that the genetic programming can successfully discover a control algorithm effectively suppressing the stick-slip. However, it is not an easy task and relatively large size of population and a big number of generations are required. Real measurement results in worse control quality. Acceleration feedback has no apparent impact on the algorithms performance, while velocity feedback is important.

Systematic Odometry Error Evaluation and Correction in a Human-Sized Three-Wheeled Omnidirectional Mobile Robot Using Flower-Shaped Calibration Trajectories

“…In both cases, the inputs and genome of the minimization functions are the initial values of the kinematic parameters 𝑝𝑝𝑎𝑎𝑟𝑟𝑎𝑎𝑚𝑚 𝑖𝑖 defined as: 𝑝𝑝𝑎𝑎𝑟𝑟𝑎𝑎𝑚𝑚 𝑖𝑖 = (0.195, 0.195, 0.195, 0.148, 0.148, 0.148, 60.000, 180.000, 300.000) (15) And the upper (𝑝𝑝𝑎𝑎𝑟𝑟𝑎𝑎𝑚𝑚 𝑢𝑢𝑏𝑏 ) and lower (𝑝𝑝𝑎𝑎𝑟𝑟𝑎𝑎𝑚𝑚 𝑊𝑊𝑏𝑏 ) bounds proposed to guarantee the physical interpretation of the results: 𝑝𝑝𝑎𝑎𝑟𝑟𝑎𝑎𝑚𝑚 𝑢𝑢𝑏𝑏 = (0.220, 0.220, 0.220, 0.158, 0.158, 0.158, 62.000, 182.000, 302.000) 𝑝𝑝𝑎𝑎𝑟𝑟𝑎𝑎𝑚𝑚 𝑊𝑊𝑏𝑏 = (0.170, 0.170, 0. 0.170, 0.138, 0.138, 0.138, 58.000, 178.000, 298.000) (16) The specific search functions used in this paper are: Fmin search function. The implementation of a gradient search nonlinear minimization to calibrate the odometry is based on the Matlab function fmincon.m, which is a nonlinear multivariable function that attempts to iteratively find the local unconstrained minimum of an objective multivariate cost function summarized in a value 𝐶𝐶𝐶𝐶 evaluated within specific bounds.…”

“…This procedure was verified with a three-wheeled omnidirectional mobile robot performing different paths. In general, the evaluation of tracking errors in offline analysis has the advantage of avoiding local minimum in complex parametric nonlinear systems [16].…”

Non-Parametric Calibration of the Inverse Kinematic Matrix of a Three-Wheeled Omnidirectional Mobile Robot Based on Genetic Algorithms

“…This proposal was based on the comparison of trajectory simulations, performed with a virtual mobile robot, with experimental trajectory measurements performed by the real mobile robot. Under such conditions, the assumption was that offline calibration of the kinematic matrix of the mobile robot was less prone to local minima effects [15]. Prados et al [16] analyzed the motion performance of a four-wheeled omnidirectional mobile robot tailored for surveillance application in limited spaces.…”