Authors: Seonghyeon Jo(cpsc.seonghyeon@gmail.com)
Date: Jan 20, 2022
This repository is a MATLAB simulation of adaptive fuzzy sliding mode control for robot manipulator. The robot manipulator uses sawyer 4-dof manipulator and prototype 3-dof manipulator. we compare to simple PID Controller, Sliding Mode Control(SMC), Fuzzy Silding Mode Control(FSMC), Adaptive Fuzzy Sliding Mode Control(AFSMC).
"Adaptive fuzzy sliding mode control using supervisory fuzzy control for 3 DOF planar robot manipulators."
In general, the dynamic of a robotic manipulator can be expressed as follows:
where
denote the joint position vector, velocity vector, acceleration, the vector of control torques, and the vector of disturbance torques, respectively, and
denotes the symmetric positive definite inertia matrix,
denotes the Coriolis matrix,
denotes the gravity vector and
is the friction matrix.
Multiplying
The sliding proportional-integral-derivative PID surface in the space of tracking error can be defined as:
where kp is positive proportional gain matrix, ki is positive integral gain matrix, kd is positive derivative gain.
Take the derivative of sliding surface with respect to time, then
The control effort being derived as the solution of s˙(t) = 0 without considering uncertainty (d(t) = 0) is to achieve the desired performance under nominal model, and it is referred to as equivalent control effort , represented by ueq(t)
| Method | joint 1 | joint 2 | joint 3 | joint 4 | sum |
|---|---|---|---|---|---|
| PID | 0.0394 | 0.0339 | 0.0044 | 0.0083 | 0.0860 |
| SMC-SIGN | 0.0078 | 0.0349 | 0.0003 | 0.0039 | 0.0469 |
| SMC-SAT | 0.0078 | 0.0358 | 0.0004 | 0.0019 | 0.0460 |
| FSMC | 0.0111 | 0.0146 | 0.0017 | 0.0043 | 0.0317 |
| AFSMC | 0.0105 | 0.0141 | 0.0013 | 0.0042 | 0.0301 |
