Adaptive Fuzzy Control of Flexible Joint Robot

Flexible joint model

Introduction to FJR

robots generally have many elastic elements in their transmission systems

So,they may result in the occurrence of tensional vibrations when a fast response is required

Joint elasticity may arise from several sources , such as elasticity in gears (Harmonic Drives HD) ,belts, tendons, bearings ,and hydraulic lines,

• Traditional robot control strategies assume joint and link rigidity

For more precision and efficiency we should include elastic dynamics in control strategies

FJR MODELING

• There are two models

• Simplified model (If the inertial couplings between

the motors and the rigid links are neglected - Spong ,1987)

• Complete model (If the couplings between the links and

the motors are included - Tomei, 1991)

Flexible joint complete model

History of filed research

Primary research During the first years of considering FJRs

(beginning of the 80’s) several papers were published. Most of them considered the following items:

1) The necessity of considering flexibility,

2) FJR modeling,

3) Simple controller design,

4) Analysis of the FJR specifications such as controllability.

Continuing the initial path

mean all methods having all or several of the following specifications:

• Using a Spong model (and accepting his assumptions).

• Using the Singular Perturbation Method for modeling.

• Using the Composite Control Strategy with a fast control term to stabilize the fast variable.

.

Papers continuing the initial path.

Control of Flexible Joint robot

• When faces an control problem , two solution approach exist in the literature :

• Model-based approach used when system model are completely known ( PID

,pole placement. …etc)

• Model-free approach used when we does not have information about the

system (ANN , FLSs …etc )

Reduction in the number of feedback quantities has been always a goal in controller design,

Papers considering the number of measurements could be classified into two classes :

• First, avoiding rate measurement by changing the control strategy

• Second using observers instead of changing the control strategy

Measurement reduction (GOOD)

type-2 fuzzy logic controller

•  From the very beginning of fuzzy sets, criticism was made about the fact that the membership function of a type-1 fuzzy set has no uncertainty associated with it

• what does one do when there is uncertainty about the value of the membership function?

• The answer to this question was type-2 FLC

Membershipe in type-2 FLC

Footprint of uncertainty (FOU)

interval type-2 fuzzy set

• For an interval type-2 fuzzy set that third-dimension value is the same (e.g., 1) everywhere.

• So, for such a set, the third dimension is ignored, and only the FOU is used to describe it.

• for this reason that an interval type-2 fuzzy set is sometimes called a first-order uncertainty fuzzy set model, whereas a general type-2 fuzzy set is sometimes referred to as a second-order uncertainty fuzzy set model.

Typical fuzzy logic controller

Block diagram of a type-2 FLS

Inference process

What I want to do

• Design a simple interval type-2 fuzzy logic system

• Chick the controller stability .

• Simulate the controller on simulation program and discuss results .

Thank you for your

attention

• Cascade fuzzy logic control of FJM

• Reduced rule-based fuzzy control of FJM

• Adaptive tracking control of FJM

5- Adaptive controllers The most important deficiency of the integral manifold approach is

lack of robustness of parametric uncertainty thus adaptive controllers have been considered since the early years in the FJR literature

• Adaptive methods in the FJR literature could be categorized into two major branches:

A ) the first approach, called the Inverse Dynamics Adaptive Approach

B ) the second approach, called the Slotine and Li Approach,

6- Robust control and stability• Several controllers based on a Lyaponov stability

analysis were developed• sliding mode configuration adding a term that would

continuously retain state on stable trajectories.

7 - Implementation issues Several industrial robots have flexible joint(s) due to the

use of a harmonic drive in their power transmission system. Among them, PUMA 560 and KUKA IR 160/161

Simplified model

• If the gear ratio is high, this is a reasonable approximation as described in, e.g., Spong (1987).

• The model equations of the simplified flexible joint model are:

• Where joint and motor angular positions are denoted

respectively.

The friction torque is here approximated as actingon the motor side only.

Complete model

• the couplings between the links and the motors are included (Tomei, 1991)