Receding Horizon Vs Finite Horizon in Planning

Question

So, I am reading a paper on TSP. In one of the papers it is mentioned:

We plan using a fixed-horizon approach, alternating between replanning and execution until the elapsed time $t$ exceeds the budget $B$

However the definition of fixed horizon in this paper research paper is mentioned as follows:

The fixed horizon approach to path planning involves computing an optimal path over the entire planning horizon

So my question is: If fixed horizon is meant to last over entire planning horizon (which I doubt) then why did the author in the paper above mentioned:

alternating between replanning and execution:

after mentioning we follow fixed horizon approach? Isnt this receding horizon approach? where you plan again and again after certain time step like in model predictive control?

Answer 1

Got a reference from Wikipedia article on MPC, which states:

The main differences between MPC and LQR are that LQR optimizes in a fixed time window (horizon) whereas MPC optimizes in a receding time window,[4] and that a new solution is computed often whereas LQR uses the single (optimal) solution for the whole time horizon.

So to grab the gist of above, fixed horizon is fixed time interval where plan is executed, and the plan is NOT recomputed until horizon is finished while receding horizon the plan gets repeatedly computed and executed.

Answer 2

I'm not positive (this isn't my area of competence), but I think in the first paper they are planning movement over a fixed spatial domain (which I guess is the "horizon"), and then refining the information or parameters and replanning over the same horizon. So it is not a receding horizon approach.