This project is aimed to the solution of optimal control problems for a differential drive robot in an environment with obstacles.
In particular two kind of tasks are solved, point stabilization and trajectory tracking.
Solutions to these Optimal Control Problems are found considering a Non Linear MPC strategy in order to minimize the power consumption of the robot and avoid possible obstacles in the environment.
Two possible direct approaches are used with the N-MPC strategy :
- Single Shooting -> It takes into account only control actions as optimization variables.
Problem formulation:
- Multiple Shooting -> It considers also trajectory states as optimziation variables.
Problem formulation:
Furthermore a comparison between these two approaches, when the same finite horizon is imposed, is given. All solutions are computed by means of fmincon in MATLAB®.
| Single Shooting | Multiple Shooting |
|---|---|
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An example of a Trajectory Tracking, solved with Single Shooting approach, is shown in the following figure:
