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Robotic Manipulators Modeling

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  • Lecturer: Faïz Ben Amar ; Viviane Pasqui (faiz.ben_amar@sorbonne-universite.fr)
  • Course code:
  • Student workload: 22 h of lectures, 8 h of tutorials
  • Credits: 3 ECTS
  • Specialization tracks: ROBOT SI MeDH
  • Semester offered: S1 S2 S3 S4
  • Language of instruction: French English
  • Targeted audience: Eng. Sc. department Other : ENSAM
  • Localization : PMC Campus Other :

Course Overview

This course unit trains students in the dynamic modeling of serial and parallel robotic manipulators and, more generally, of multibody systems connected by bilateral joints and involving unilateral frictional contacts with the environment, such as walking robots and multi-fingered grippers.

Mots-clés : Kinematics of serial and parallel robotic manipulators, forward and inverse models, geometric wrenches, singularities, redundancy and optimization. Principle of virtual work, generalized coordinates, generalized forces, holonomic and nonholonomic constraints, Lagrange equations, Lagrange multipliers, Cartesian versus joint parameterization, quaternions, solution of differential-algebraic equations, parameter changes, partitioning and parameter reduction, unilateral contact, friction models and nonsmooth dynamics

Prerequisites

Students should have previously acquired the following prerequisites to follow this course:

  • Parameterize a serial robot using the DH convention and master rotation matrices and homogeneous transformations
  • Calculate the kinetic and potential energy of a rigid body and write the mass matrix of a rigid-body system
  • Write the Jacobian of a rigid body and calculate a generalized force

Intended Learning Outcomes

By the end of this course, students will be able to:

  1. Analyze the mobility and static indeterminacy of a mechanism or parallel robot
  2. Identify the singularities of parallel robots and write their geometric or kinematic models
  3. Identify the different terms in the equations of motion
  4. Reduce a model parameterization
  5. Solve a differential-algebraic system
  6. Model joints involving unilateral frictional contact
  7. Write the dynamic model of a tree-structured, parallel or hybrid system
  8. Compare the advantages and disadvantages of different parameterizations according to the intended use of the model
  9. Model a system with unilateral contacts

Indicative Teaching Sequence and Methods

Week C/TD/TP* Content Preparation Learn.\ outc.
S1 Lecture Kinematics of serial robots, geometric wrenches, Jacobian, singularities AAV1
S2 Lecture Kinematics of serial robots, redundancy and optimization AAV1
S3 TD Kinematics of serial robots AAV1
S4 Lecture Kinematics of parallel robots, mechanism theory AAV2
S5 Lecture Kinematics of parallel robots, models, singularities AAV2
S6 TD Kinematics of parallel robots AAV2
S7 Lecture Lagrangian dynamics: principle of virtual work, generalized coordinates and forces, holonomic and nonholonomic constraints AAV7
S8 Lecture Lagrangian dynamics: Lagrange equations with and without multipliers AAV7
S9 TD Lagrange equation: serial robot AAV7
S10 TD Lagrange equation with multipliers: parallel robot AAV3
S11 Lecture Multibody systems: Cartesian versus joint parameterization AAV8
S12 Lecture Multibody systems: Cartesian parameterization and quaternions AAV8
S13 Lecture Solution of differential-algebraic equations AAV5
S14 Lecture Unilateral contact and friction AAV9
S15 TD Lagrange equation: nonholonomic mobile robot or humanoid robot AAV9
  • C/TD/TP respectively corresponds to lectures, tutorials and lab sessions.

Indicative Assessment of Intended Learning Outcomes (1st session)

Week Individ./group In-person/remote Type of exam Evaluated outcomes Scale %
S8 Individual In-person Written exam 50%
S16 Individual In-person Written exam 50%

2nde session

Session Individ./group In-person/remote Type of exam Evaluated outcomes Scale %
2 Individual In-person Written exam All 100%

Logo SDI Date of generation of this unit description: 06/10/2026 Logo SDI