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# 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. Control
- 7. Cubic Configuration (link)
- 8. Bibliography (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. The git repository of the project is accessible here.

## 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 is explained 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 Control

The use of active control for Stewart platforms is a wide subject. Many aspect can be studied.

The sensors used is of primary important. We can have:

- Sensors located in each strut: relative motion, force sensor, inertial sensor
- Sensors measuring the relative motion between the fixed base and the mobile platform
- Inertial sensors located on the mobile platform

The control objective can also vary:

- Reference Tracking
- Active Damping
- Vibration Isolation

The Control for Stewart platforms is here studied in the following files:

- Active Damping (link). The use of different sensors are compared for active damping:
  - Inertial Sensor in each strut or fixed to the mobile platform
  - Force Sensor in each strut
  - Relative Motion Sensor in each strut
- Motion Control (link). Different control architectures (centralized and decentralized) are compared for the position control of the Stewart platform.
- Vibration Isolation (link)

## 7 Cubic Configuration (link)

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

These properties are studied in this document.

## 8 Bibliography (link)

Many text books, PhD thesis and articles related to parallel robots and Stewart platforms are gathered in this document.

Author: Dehaeze Thomas

Created: 2021-01-08 ven. 15:30