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Module IN2067

This Module is offered by TUM Department of Informatics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2015/6

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2022WS 2015/6SS 2012

Basic Information

IN2067 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
180 h 75 h 6 CP

Content, Learning Outcome and Preconditions


On the one hand, this module presents a method how a mechanical system can be converted into a mathematical system of equations for analysis of motion. In a second step, the parameterization of the control of a manipulator is derived from the mathematical analysis of the above equation in order to compensate for any errors and deviations along a given trajectory.

The following topics are defined in the lecture and discussed using practical examples:
- Coordinate systems (Denavit-Hartenberg convention)
- Forward kinematics (relationship: joint rotation to manipulator motion)
- Inverse kinematics (relationship: manipulator motion to joint rotations)
- Newton-Euler/Lagrange analysis of the dynamic state in the joints
- Dynamic modeling of the manipulator (mathematical model (MVG) for motion analysis)
- PID control of position and force

Learning Outcome

The participants should be able to create a mathematical model of a mechanical system using force/torque analysis (Newton-Euler approach) or by energy analysis (Lagrange method), which relates the drive torques in the joints to motion parameters of the manipulator.
They should also be able to explain the meaning and mathematical relationship to the above model for the control parameters of a PID controller for a robotic system and determine their optimal values for a position and force controller.


- Vector algebra
- Differential calculus
- Basic knowledge of physics (Newton's Law, etc.)

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VI 5 Robotics (IN2067) Burschka, D. Tue, 09:00–12:00, Interims I 101
Mon, 14:00–16:00, Interims II 004

Learning and Teaching Methods

The course content is presented to the students in a lecture and deepened in an interactive discussion. There are also recorded lectures from previous years that can be used for self-study. The individual learning is supported by tutorials, which are to be solved independently by the students and then their solutions are presented in a 2-hour exercise.
Practical examples from the industry on the presented topics will also be shown and guest lectures from the industry will be organised.


Blackboard, slides, videos and online examples


Introduction to Robotics Mechanics and Control John
J, Craig, Prentice Hall. ISBN 0-13-123629-6

Module Exam

Description of exams and course work

In a 90-minute written exam, participants must create a mathematical model of a kinematic chain of a given manipulator, determine the relationship between the required forces and torques in the actuator and the dynamic state of the robot, and design a stable PID controller for an exemplary task design that is described in the problem.

Exam Repetition

The exam may be repeated at the end of the semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

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