Realistic Animation of Articulated Bodies

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Credits
3
Types
Elective
Requirements
This subject has not requirements, but it has got previous capacities
Department
FIS
Web
www-fen.upc.es/~arca
The aim of this subject is give students an understanding of physics in order to enable them to build physically realistic mathematical models of articulated systems (robots, vehicles, animated bodies with skeletons, etc.).

Numerical integration and optimization methods will be used for obtaining the resulting movement, yielding a physically realistic animation out of the dynamics equations of the system studied.

Teachers

Person in charge

  • Joaquim Casulleras Ambros ( )

Weekly hours

Theory
2
Problems
1
Laboratory
1
Guided learning
0
Autonomous learning
7

Objectives

  1. To know how to develop a mathematical model of an articulated body system.
    Related competences: CTR6,
  2. Mastering the Denavit-Hartenberg formalism.
    Related competences: CTR6, CG4, CG8,
  3. Learn to adapt and extend the DH formalism to describe the physical properties and mass distribution of an articulated body.
    Related competences: CTR6, CG8,
  4. To understand and properly use the laws of dynamics of articulated systems.
    Related competences: CTR6, CG4,
  5. Knowing how to use the Lagrange formalism to find static and dynamic equations.
    Related competences: CG8,
  6. Being able to identify and determine the relevant physical quantities (generalized coordinates and moments) of the dynamics in the Lagrangian formulation.
    Related competences: CTR6,
  7. To be able to Identify the relevant variables in systems subject to restricted dynamic conditions.
    Related competences: CTR6,
  8. Knowing how make use of the Lagrange formalism in dynamics under restricted conditions.
    Related competences: CG8,
  9. To know and make proper use of computer mathematical methods for the integration of dynamic equations.
    Related competences:
  10. Being able to establish the generalized forces from an optimization problem of the cost function.
    Related competences: CG8,
  11. To be able to establish a cost function based on the generalized coordinates and moments that allow discriminating among the physically valid solutions, those that best suit the saught movement.
    Related competences: CTR6,
  12. Being able to create a physically realistic animation, based on an optimization process under the conditions dictated by the dynamics equations.
    Related competences: CTE7, CTE10, CTE12, CTR6, CG4, CG8,

Contents

  1. Articulated rigid bodies systems. Denavit-Hartenberg Formalism.
  2. Lagrange Dynamics. Generalized coordinates and momenta. Dynamics equations.
  3. Constraint conditions. Equations for constrained movements.
  4. Optimization. Objective function. Optimal physically realistic evolution generation.

Activities

Activity Evaluation act


Development of theme 1 of the course


Objectives: 2
Contents:
Theory
4h
Problems
1h
Laboratory
0h
Guided learning
0h
Autonomous learning
2h

Development of theme 2 of the course


Objectives: 8
Contents:
Theory
3h
Problems
1h
Laboratory
0h
Guided learning
0h
Autonomous learning
2h

Development of item 3 of the course


Objectives: 8 7
Contents:
Theory
4h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
2h

Development of theme 4 of the course


Objectives: 12
Contents:
Theory
3h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
2h

Final Exam

Written exercise.
Objectives: 2 8 12 1 3 4 5 7 6 9 10 11
Week: 7
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
6h

Continuous assessment.

Evaluation of exercises presented in class.
Objectives: 2 1 3 4
Week: 4
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Continuous assessment.

Evaluation of exercises presented in class.
Objectives: 2 8 12 1 3 4 5 7 6 9 10 11
Week: 7
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Lab work

Development of a lab activity.
Objectives: 2 8 12 1 3 4 5 7 6 9 10 11
Week: 7
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
2h
Autonomous learning
8h


Study and preparatory work for lab sessions.

Students will study the material provided, and on the basis of the theoretical tools explained in class, prepare work to be held in the laboratory.
Objectives: 2 8 12 1 3 4 5 7 6 9 10 11
Contents:
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
10h


Teaching methodology

The teaching methodology will be based on theory classes, classes of problems, practical exercises, and a practical session covering computer animation and drawing upon the knowledge acquired during the course and on basic numerical computer calculation.

Evaluation methodology

The evaluation will consider three aspects:
- Continuous assessment of work done during the course, in solving exercises proposed in class.
- Evaluation of a lab exercise.
- An exam (theory and problems).

The course grade will be calculated according to the following weighted average:

course grade = 0.2 Continuous assessment + 0.4 lab grade + 0.4 exam grade

The assessment of competence CTR6 will be computed as the arithmetic mean of the grades assigned to this competence in the final exam and in the continuous assessment of course work.

Bibliography

Basic:

  • Apunts de teoria de Animació Realista de Cossos Articulats - Casulleras, J,

Complementary:

  • Col.lecció d'exercicis i problemes en Animació Realista de Cossos Articulats - Casulleras, J, , .

Previous capacities

Knowledge of mathematical analysis. Vector and matrix formalism. Notions of differential calculus.