Receding Horizon Control

Definition

Receding horizon control (RHC) repeatedly solves an optimization over a short, finite look-ahead
horizon of $N_H$ steps, executes only the first portion of the resulting plan, then re-solves from the
updated state — so the horizon “recedes” as the system advances (naumann2020probabilistic).
It is the planning view of model predictive control: the two names denote
the same iterate-replan loop. The finite horizon keeps an otherwise long- or infinite-horizon, nonlinear
problem tractable and lets new sensor data enter at each replan; the price is that optimality over the
true (full) horizon is not guaranteed. Both cited sources are terrestrial / aerial robotics
(automated driving and a micro-aerial-vehicle), not space systems — neither addresses the free-flying
base or its dynamic coupling.

Key Equations

Symbols per notation.md.

Over a receding horizon the utility sums only the next $N_H$ stage rewards $r(s_i)$, which bounds an
otherwise unbounded long-horizon objective (naumann2020probabilistic):

$R_{\mathrm{RH}}(\tilde{\mathbf{s}})={\sum }_{i=0}^{N_H}r(s_i),R_{\mathrm{RH}}\le (N_H+1)r_{\max }.$

The loop is then: at state $s$, choose the action sequence maximizing $R_{\mathrm{RH}}$, apply its first
step, advance, and repeat. (Symbols $s_i$ stage/state, $r(\cdot )$ stage reward, $N_H$ horizon length,
$r_{\max }$ per-step reward bound are local to this discrete-decision setting and are not in
notation.md, which is keyed to the continuous FFSM dynamics — flagged, not silently conflated.)

Source Support

• naumann2020probabilistic — primary definitional source: states MPC “is also called receding horizon control,” gives the iterate-execute-first-step-replan mechanism and the bounded finite-horizon reward $R_{\mathrm{RH}}$; framed for automated-driving motion planning.
• papachristos2019localization — applies the receding-horizon planning paradigm to aerial-robot exploration: a two-layer sampling-based planner repeatedly picks the next-best viewpoint ${\xi }_{RH}$, optimizes a belief-uncertainty path to it (D-optimality metric $D_{opt}$), executes it, and re-plans (merged here from the former receding_horizon_planning split).

Related Topics

• model_predictive_control — same control loop under its optimal-control name; RHC is the planning-side label for MPC’s receding window.
• nonlinear_mpc — the nonlinear instance the receding horizon is specifically meant to tame, per naumann’s motivation.
• motion_planning_under_uncertainty — the replan loop is the standard vehicle for feeding belief/uncertainty updates back into planning (papachristos’ belief-space replanning).
• chance_constraints — the per-replan optimization is where probabilistic safety constraints are imposed in a risk-aware RHC.
• receding_horizon_planning — the sampling-based planning facet (papachristos’ RHEM); overlaps strongly with this page (see Open Questions).

Open Questions

• Both sources are terrestrial/aerial; does the receding-horizon loop’s short-horizon tractability argument still hold for a free-flying space manipulator, where base–arm dynamic coupling can make even a short prediction nonlinear and stiff?
• naumann notes RHC forfeits true-horizon optimality; for our inspection task does the per-replan reward (e.g. coverage / next-best-view gain) need an explicit terminal-cost or horizon length tied to the manipulability/singularity margin to avoid myopic, near-singular plans?
• This page and receding_horizon_planning cover nearly the same idea (control-loop vs sampling-planner facet) — should they be merged outright, or does keeping the planning facet separate earn its keep?