Some constraints are probabilistic in nature. Noisy image measurements are a constraint of this sort, they influence the dynamic model but do not impose hard constraints on its behavior.
Soft constraints such as these can be expressed as a potential field acting on the dynamic system. The incorporation of a potential field function that models a probability density pushes the dynamic evolution of the model toward the most likely value, starting from the current model state.
Note that functions that take the model state as input, such as a the
controller from Section 2.2.3, can be represented as a
time-varying potential field. One relevant example is incorporation
of a probability distribution over link position and velocity:
