Motion planning for mechanical systems

MSc in Computer Science and Engineering

Prof. Paolo Rocco

 

Schedule

The course is offered in the second semester

 

 

Learning objectives and course syllabus

The goal of this course is to provide the students with a general overview of the methodologies for planning and control of motion of mechanical systems. Kinematics of the body and of the systems of bodies, interaction of the bodies with the environment, prediction of motion through the dynamic model, and motion control will be addressed in the course, making frequent reference to the case of robotic arms.

A mix of theoretical and industrially relevant topics characterizes the course, where extensive use of software for modelling and simulation of mechanical systems will be made.

 

Course syllabus is as follows:

1. Introduction

Introduction to the motion systems with examples 

 2. The description of motion: kinematics of bodies and systems of bodies

Position and orientation of a rigid body. Roto-translations. Velocity of a body. Direct, inverse and differential kinematics of a robotic manipulator.

 3. The interaction of bodies with the environment

Forces at the contact, statics of bodies and systems of bodies. Application to robots in contact with the environment.

4. The explanation and the prediction of motion: dynamics of bodies and systems of bodies

Newton-Euler equations for bodies and Lagrange equations for systems of bodies. Application to modelling and simulation of drones and of robots

5. The planning of motion

Path and trajectory generation for single bodies and articulated structures. Trajectories in the joint space and in the operational space for a robot. Elements of robot programming.

6. The methods for motion sensing

Position sensing: resolvers and encoders. Algorithms for velocity estimation from position measurements.

7. The control of motion

How to make a system of bodies track a prescribed motion. Application to robotics.

 

Prerequisites

Basics in Linear Algebra, Automatic Control and Mechanics.

 

Bibliography

B. Siciliano, L. Villani, G. Oriolo, A. De Luca: Foundations of Robotics., Springer, 2025 (in English)

 

Lecture notes

Lecture notes are available in the WeBeep channel for students enrolled in the course.

 

Lab sessions with MATLAB/Simulink/Robotics Toolbox

In order to participate in the lab activities, students need to bring their own laptop with them.

You need to install your own copy of MATLAB/Simulink. Instructions how to download and install your free copy of MATLAB are available here:

https://www.software.polimi.it/mathworks-matlab/?lang=en

You also need to install an additional toolbox, the Robotics Toolbox by Peter Corke. The instructions to download and install the toolbox (latest release is 10.4) are available at:

https://petercorke.com/toolboxes/robotics-toolbox/

Please notice that this is not the toolbox on robotics delivered by The MathWorks. Functionalities of the toolbox have been checked with success with recent versions of MATLAB until R2019b.

A manual of the toolbox is available.

Depending on the way you installed the toolbox, in order to run the toolbox you may need to issue the initialization command:

startup_rvc



Exams

Students will take a written examination, integrated by an oral one at the instructor's discretion. Text of the exam will be in English, solutions should preferably be given in English.

Texts of exams are published here.

August 31, 2026 Text

July 20, 2026 Text Solutions

June 18, 2026 Text Solutions