Composable Controllers for PhsicsBased Character Animation

[source] Siggraph

[year] 2001

物理动画的大目标：虚拟人物自动合成真实动作，且拥有丰富的技能

a framework of composing controllers in order to enhance the notor abilities of such figures.

an explicit model of the “pre-conditions” under wihich moter controllers are expected to function properly.

分治原则

分了很多了，说好的治呢？

本framework：

每个单独的controller视为blackbox,但要有： 1.able to determine whether or not it can take the dynamic character from its current state to some desired goal state. 2.to determine whether it is operating normally, whether succeeded or not.

Previous Work

    Biomechanics     Robotics     Computer Animation       Dynamically Simulated Articulated Figure

3. Controller Composition Framework

3.1 Controller Abstraction

      pre-cond.                  post-cond.                    expeted performance

      if pre-cond.s are met then the controller can operate and possible enable the character to satisfy the post-cond.s

      ie. mapping from a domain of input states to a range of output states

3.2 Pre-Cond.s

      in general , are realtionships and constraints

    为 :    1. init state q_i  of figure            2.environment parameters C_e.      include cotact points and normal of ground and firction   3.balance of figure C_b(S,g,c,\dot c) 一般为重心c与base of support S的相对位置及相对速度， 如果沿重力g投影落在S外，则unbalance   4.target state q_t 

     P = C(R(q_i), R(q_t), C_b, C_e)

3.3 Post-Cond.s

      O = C（R(q_0）,C_b, C_e). R(q_0)目标区域

3.4 Expected Performance

[t_1, t_2]  ,\Epsi(t_1) \in P  \Espi(t_2) \in O

3.5 Transitions

4 Determining Pre-Cond.s

4.1 Manual Approach

  A—>B –>C 则A的Post-Cond. 与B的Pre-Cond及B..与C…

   对Pre-Cond.加噪声，不断测试可能可以产生一个适当的Pre_cond.及类似的Post-Cond.

4.2自动的、学习的方法

  4.2.1 SVM

            l个观测，d维， x_i \in R^d , i=1,…,l  及相应 y_i \in {-1,1}

   4.2.2应用SVM

           x_i : init state 从此状态开始数值模拟

   4.2.3结果