#+TITLE: Stewart Platforms
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* Introduction                                                       :ignore:
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.

* Simulink Project ([[file:simulink-project.org][link]])
The project is managed with a *Simulink Project*.
Such project is briefly presented [[file:simulink-project.org][here]].

* Stewart Platform Architecture Definition ([[file:stewart-architecture.org][link]])
The way the Stewart Platform is defined [[file:stewart-architecture.org][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

* Simscape Model of the Stewart Platform ([[file:simscape-model.org][link]])
The Stewart Platform is then modeled using [[https://www.mathworks.com/products/simscape.html][Simscape]].

The way to model is build and works is explained [[file:simscape-model.org][here]].

* Kinematic Analysis ([[file:kinematic-study.org][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 [[file:kinematic-study.org][here]].

* Identification of the Stewart Dynamics ([[file:identification.org][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 [[file:identification.org][here]].
 
* Active Damping ([[file:active-damping.org][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 [[file:active-damping.org][here]].

* Motion Control of the Stewart Platform ([[file:control-study.org][link]])
Some control architecture for motion control of the Stewart platform are applied on the Simscape model and compared in [[file:control-study.org][this]] document.

* Cubic Configuration ([[file:cubic-configuration.org][link]])
The cubic configuration is a special class of Stewart platform that has interesting properties.

These properties are studied in [[file:cubic-configuration.org][this]] document.

