What are the downsides of disabling homotopy class planning in Teb Planner ?

edit

To add to this answer:

teb uses NLP (Non-linear Programming) to calculate paths. NLP is an optimization technique that starts from a 'guess solution' and iteratively find better solutions until termination criteria are met. NLP uses a cost function and its gradients to do this. The cost function combines multiple criteria eg. obstacle separation, vehicle constraints and travel time. NLP is local, meaning it converges to the solution nearest to the starting guess. Obstacles cause multiple local minima to exist, therefore the solver could give sub-optimal or infeasible solutions, while better trajectories exist.

That is where the homotopy classes come in: every path in the same homotopy class will converge to the same final result. teb constructs a candidate path in every discovered homotopy class and optimises all of them, selecting the path with the lowest cost function value. Disabling homotopy class planning can lead to suboptimal or infeasible paths.

Also, looking at the bottom of the FAQ, the author suggests that 2 homotopy classes might be enough for most cases.