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Lecture 18: Animation of Articulated Figures

Lecture 18: Animation of Articulated Figures. Kinematics. Animating Articulated Structures become popular because The desire to use human beings as synthetic actors in 3D computer animation environments

kristian-vidar
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Lecture 18: Animation of Articulated Figures

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  1. Lecture 18: Animation of Articulated Figures

  2. Kinematics • Animating Articulated Structures become popular because • The desire to use human beings as synthetic actors in 3D computer animation environments • KINEMATICS is the study of the motion of a body or body segment without reference to the forces that act on the system.

  3. Forward Kinematics • Forward Kinematics is the process of calculating the position in space of the end of a linked structure, given the angles of all the joints. It is easy, and there is only one solution. Forward Kinematics X = f() That is, given , derive X

  4. ? End Effector Base What is Forward Kinematics? • Forward Kinematics X = f()

  5. Inverse Kinematics • Inverse Kinematics does the reverse. Given the end point of the structure, what angles do the joints need to be in the achieve that end point. It can be difficult, and there are usually many or infinitely many solutions. Inverse Kinematics  = f-1(X) That is, given X, derive 

  6. End Effector Base What is Inverse Kinematics? • Inverse Kinematics  = f-1(X)

  7. Forward Kinematics • This Chain is represented here, without any information about its actual shape, what we are interested in is the relative positions of all the joints. • The first link is the base (or "anchor point") is the end of the chain which always has a fixed or known position. • From there, each link can be rotated (possibly in different dimensions depending on the degree of freedom of the joint).

  8. Inverse Kinematics • For inverse kinematics (IK), the position of the end point is known, and we need to find the angles of the joints. This is a much harder problem, there may be many possible answers • There are two approaches to solving inverse kinematics: • Analytical - requires a lot of trigonometry or matrix algebra • Iterative - better if there are lots of links and degrees of freedom.

  9. Analytic solution of 2-link inverse kinematics x2 y2 (x,y) O2 2 y0 y1 a2 2 x1  a1 O1  1 x0 O0

  10. Inverse Kinematics • Start off with the joints in any position, then move each of the joints in turn, so that each movement takes the endpoint toward the target. • Starting with the joint nearest the end point, rotate the joint so that the current end point moves toward the required end point. Then do the same with the next joint toward the base and so on until the base is rotated. Then keep repeating this, until the end point is close enough to the required end point or if further iterations are not moving it closer to the required point.

  11. Inverse Kinematics • It may be possible to have a more realistic strategy than this, for instance, if I am using my arm to pick up an object then, if the object is a long way away, I will move the bigger joints in the arm, then as the hand gets closer the smaller joints of the hand are used for the fine adjustments.

  12. Inverse Kinematics • The angle of rotation for each joint is found by taking the dot product of the vectors from the joint to the current point and from the joint to the desired end point. Then taking the arccos (cos-1) of this dot product. • To find the sign of this angle (ie which direction to turn), take the cross product of these vectors and checking the sign of the Z element of the vector.

  13. Degree of Freedom (DOF) • The dofs define the independent relative motions allowed • Each joint can include a combination of: - 3 translation dofs - 3 rotation dofs

  14. Degree of Freedom (DOF)

  15. Degree of Freedom (DOF)

  16. Articulated Figure • A structure that consists of a series of rigid links connected at joints

  17. Kinematic graph • The kinematic graph defines the structure of the articulated body

  18. Data Structures • Kinematic graph: • List of root joints (one/articulated body) • Nodes: joints and solids • Solid: • Parent joint • List of child joints • joints • Parent solid • child solid • Transform wrt parent • Dofs (eg: translation, rotation…)

  19. Failures of simple IK • In many cases, it will be impossible for the linked structure to touch the target. For example, you cannot touch your elbow with your hand and you cannot reach the top of a tall tree from the ground. In some unstable cases: the target moves far out of range of the structure.

  20. Failures of simple IK • No Solution

  21. Failures of simple IK • One Solution

  22. Failures of simple IK • Two Solution: If there are two solutions, this technique will find which ever is closest to the current state of the structure.

  23. Failures of simple IK • Many Solution: When there are more than two joints, there will frequently be infinitely many solutions to the problem. However, some solutions will be better than others. If your structure represents an arm for example, some solutions will look more comfortable and others very strained. There is often an optimal solution.

  24. Failures of simple IK • Multiple Solutions

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