To motivate the introduction of constraints, consider a control model proposed in [235,830]. The action space, defined as in Formulation 8.2, produces a velocity for each action . Therefore, . Suppose instead that each action produces an acceleration. This can be expressed as , in which is an acceleration vector,
Suppose that a vector field is given in the form . How can a feedback plan be derived? Consider how the velocity vectors specified by change as varies. Assume that is smooth (or at least ), and let
(8.46) |
Now the relationship between and will be redefined. Suppose that is the true measured velocity during execution and that is the prescribed velocity, obtained from the vector field . During execution, it is assumed that and are not necessarily the same, but the task is to keep them as close to each other as possible. A discrepancy between them may occur due to dynamics that have not been modeled. For example, if the field requests that the velocity must suddenly change, a mobile robot may not be able to make a sharp turn due to its momentum.
Using the new interpretation, the difference, , can be considered as a discrepancy or error. Suppose that a vector field has been computed. A feedback plan becomes the acceleration-based control model
Steven M LaValle 2020-08-14