Optimization problem classification

[jumbo1985]

Here all,

Here's a problem I'm trying to solve.

Given a planar piecewise linear and circular curve (ie. a curve consisting of line and circular arc segments) that represents the path of a particle; a set of rules for traversing the two types of curve segments as well as the transitions between the segments by my particle and finding the travel time (ie the speed is not constant); bounds on jerk/acceleration/velocity

I want to find another planar piecewise linear and circular curve satisfying a set of criteria (described non-rigorously just to provide some context) such as:
- closeness to the original curve
- minimizing the total travel time
- minimizing the jerk experienced by particle

If there are more than one curves satisfying my constraints that is OK.

Which type of optimization does this problem fall under?

I'm looking for some guidance so that I could start reading up on the relevant topics/mathematical tools. I can update the description with more details if necessary.

Thanks!

 

[andrewkirk]

I would have thought that, if the curve is piecewise linear and circular, the jerk cannot be minimised as it will be infinite at every point where motion changes from linear to circular and vice versa - unless the particle comes to an absolute stop at every such point before proceeding.

I think your problem specification will need to allow a third type of curve section, which is curved but not circular, to allow for a finite jerk to change motion between linear and circular. You may wish to specify limits on how long such 'connecting' sections can be.

 

[jumbo1985]

I forgot to mention that the output curve is to be tangent-continuous. The motion profile will be selected so that jerk is bounded.

So far, Optimal Control seems to be the dominant theory for solving this type of a problem (assuming I have the complete set of rules for motion) as far as mathematical optimization tools.