We present simplied techniques to simulate and control complex motions. The spacetime constraint paradigm has proven successful for providing animators with control of motion without burdening them with explicit denition of the motion trajectories. Unfortunately, this method suers from undue computational complexity as the creatures or motions approach those one wouldlike to animate. Some of these problems have recently been addressed, but it is worth taking a closer look to see if simplications of the problem statement itself can be made. This extended abstract presents some experiments in decomposing the spacetime constraint formulation into smaller and simpler subproblems. Each subproblem can then be solved with an appropriate numerical methodology or perhaps through an analytic formulation. The key to this is a close examination of the physical principles in an attempt to nd assumptions which do not unduly restrict the motion, yet provide quick and simple solution methodologies. In particular, physical relationships such as angular momentum conservation laws are pulled out of the nonlinear optimization problem so that the original problem leads to a much simpler optimization problem (without the conservation equation) and two point boundary problems. By, in addition, approximating the energy minimization objective fair sized problems can be solved in real time. A human-like diving motion is used to illustrate these concepts. Experimental results are shown. Some thoughts on how to generalize this approach are given.
[1]
S. M. Roberts,et al.
Two-point boundary value problems: shooting methods
,
1972
.
[2]
L. Finkelstein.
Modern Introduction to Classical Mechanics and Control
,
1976
.
[3]
C. Frohlich.
Do springboard divers violate angular momentum conservation
,
1979
.
[4]
Andrew P. Witkin,et al.
Spacetime constraints
,
1988,
SIGGRAPH.
[5]
P. Krishnaprasad.
Geometric Phases, and Optimal Reconfiguration for Multibody Systems
,
1990,
1990 American Control Conference.
[6]
Zexiang Li,et al.
Dynamics and optimal control of a legged robot in flight phase
,
1990,
Proceedings., IEEE International Conference on Robotics and Automation.
[7]
Jessica K. Hodgins,et al.
Animation of dynamic legged locomotion
,
1991,
SIGGRAPH.
[8]
Michael F. Cohen,et al.
Interactive spacetime control for animation
,
1992,
SIGGRAPH.
[9]
Mahmut Reyhanoglu,et al.
Planar Reorientation Maneuvers of Space Multibody Systems Using Internal Controls
,
1992
.
[10]
S. Sathiya Keerthi,et al.
Optimal control of a somersaulting platform diver: a numerical approach
,
1993,
[1993] Proceedings IEEE International Conference on Robotics and Automation.
[11]
Zicheng Liu,et al.
Hierarchical spacetime control
,
1994,
SIGGRAPH.
[12]
V. Leitáo,et al.
Computer Graphics: Principles and Practice
,
1995
.