# Stewart Platforms

## Table of Contents

- 1. Simulink Project (link)
- 2. Stewart Platform Architecture Definition (link)
- 3. Simscape Model of the Stewart Platform (link)
- 4. Kinematic Analysis (link)
- 5. Identification of the Stewart Dynamics (link)
- 6. Active Damping (link)
- 7. Motion Control of the Stewart Platform (link)
- 8. Cubic Configuration (link)

The goal of this project is to provide a Matlab/Simscape Toolbox to study Stewart platforms.

The project is divided into several section listed below.

## 1 Simulink Project (link)

The project is managed with a Simulink Project. Such project is briefly presented here.

## 2 Stewart Platform Architecture Definition (link)

The way the Stewart Platform is defined here.

All the geometrical parameters are defined including:

- Definition of the location of the frames
- Location/orientation of the limbs
- Size/inertia of the platforms and the limbs

Other parameters are also defined such as:

- Stiffness and damping of the struts
- Rest position of the Stewart platform

## 3 Simscape Model of the Stewart Platform (link)

The Stewart Platform is then modeled using Simscape.

The way to model is build and works is explained here.

## 4 Kinematic Analysis (link)

From the defined geometry of the Stewart platform, we can perform static analysis such as:

- Jacobian Analysis that links the velocity of each limb to the velocity of the mobile platform
- Static Forces Analysis that links the forces applied by each limb to the resulting force/torque applied to the mobile platform

From the strut stiffness, we can also perform a Stiffness Analysis that consists of determining the Stiffness matrix and Compliance matrix of the Stewart platform from the geometry.

All these analysis are described here.

## 5 Identification of the Stewart Dynamics (link)

The Dynamics of the Stewart platform can be identified using the Simscape model.

It is possible to:

- Determine the dynamics from the actuators to the various sensors included in the Stewart platform
- Extract State Space models for further analysis / control synthesis
- Extract the Resonant Frequencies, Modal Damping, and associated Mode Shapes

The code that is used for identification is explained here.

## 6 Active Damping (link)

The use of different sensors are compared for active damping:

- Inertial Sensor in each strut
- Inertial Sensor fixed to the mobile platform
- Force Sensor in each strut
- Relative Motion Sensor in each strut

The result of the analysis is accessible here.

## 7 Motion Control of the Stewart Platform (link)

Some control architecture for motion control of the Stewart platform are applied on the Simscape model and compared in this document.

## 8 Cubic Configuration (link)

The cubic configuration is a special class of Stewart platform that has interesting properties.

These properties are studied in this document.

Author: Dehaeze Thomas

Created: 2020-01-29 mer. 20:24