Realistic Animation of Articulated Bodies

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Credits
3
Types
Elective
Requirements
This subject has not requirements

Department
FIS
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

Competences

Technical Competences of each Specialization

Especifics

  • CTE7 - Capability to understand and to apply advanced knowledge of high performance computing and numerical or computational methods to engineering problems.
  • CTE10 - Capability to use and develop methodologies, methods, techniques, special-purpose programs, rules and standards for computer graphics.
  • CTE12 - Capability to create and exploit virtual environments, and to the create, manageme and distribute of multimedia content.

Generic Technical Competences

Generic

  • CG4 - Capacity for mathematical modeling, calculation and simulation in technology and engineering companies centers, particularly in research, development and innovation tasks in all areas related to Informatics Engineering.
  • CG8 - Capability to apply the acquired knowledge and to solve problems in new or unfamiliar environments inside broad and multidisciplinary contexts, being able to integrate this knowledge.

Transversal Competences

Reasoning

  • CTR6 - Capacity for critical, logical and mathematical reasoning. Capability to solve problems in their area of study. Capacity for abstraction: the capability to create and use models that reflect real situations. Capability to design and implement simple experiments, and analyze and interpret their results. Capacity for analysis, synthesis and evaluation.

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: CG4, CG8, CTR6,
  3. Learn to adapt and extend the DH formalism to describe the physical properties and mass distribution of an articulated body.
    Related competences: CG8, CTR6,
  4. To understand and properly use the laws of dynamics of articulated systems.
    Related competences: CG4, CTR6,
  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, CG4, CG8, CTR6,

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

Development of theme 1 of the course

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

Development of theme 2 of the course

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

Development of item 3 of the course

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

Development of theme 4 of the course

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

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

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.

Bibliografy

Basic:

  • Apunts de Teoria de Animació Realista de Cossos Articulats - Casulleras,.J, , . ISBN:

Complementary:

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

Previous capacities

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