Receding-Horizon Planner

Updated 28 December 2025

Receding-horizon planning is an optimization-based strategy that repeatedly solves a finite-horizon control problem to compute adaptive action sequences under dynamic constraints.
It employs diverse methods—from classical MPC to stochastic, graph-based, and hybrid approaches—to serve applications in robotics, energy scheduling, and multi-agent systems.
By ensuring recursive feasibility, stability, and real-time responsiveness, these planners robustly handle uncertainties and strict constraints in dynamic environments.

A receding-horizon planner is an optimization-based control or planning strategy in which, at each decision epoch, an optimal plan or action sequence is computed over a finite prediction window into the future. Only the first part of this solution is implemented, after which the process is repeated using updated state estimates and potentially refined predictions. This framework, which underpins Model Predictive Control (MPC) and related online planning methods, is foundational in robotics, autonomous systems, transportation, energy scheduling, and multi-agent domains, providing a principled means to realize robust, adaptive, and constraint-aware behavior.

1. Core Principles of Receding-Horizon Planning

At the heart of receding-horizon planning is the repeated solution of an optimal control or planning problem over a finite horizon that "recedes" forward in time as feedback is obtained. At each time $t$ , the system state is measured or estimated, and a finite-horizon optimal control problem is solved: $\min_{u_{t:t+H-1}} \sum_{k=0}^{H-1} \ell(x_{t+k}, u_{t+k}) + V_{\text{term}}(x_{t+H})$ subject to system dynamics $x_{t+k+1} = f(x_{t+k},u_{t+k})$ , and any physical, safety, or task-specific constraints. Only the control $u_t$ (or a short segment) is executed, then the system advances to $x_{t+1}$ and replanning occurs with the new state (Bergman et al., 2019, Zhang et al., 2021, Ghahremani et al., 2021, Lathrop et al., 23 Nov 2024).

Key structural features are:

Rolling window: Only a short future span is optimized and implemented.
Feedback incorporation: Measurements or predictions update the problem at each receding step.
Constraint handling: Input, state, and task constraints (e.g., safety, logical objectives) can be embedded directly.

2. Algorithmic Formulations and Implementation Variants

Receding-horizon planners admit several algorithmic instantiations, varying in their treatment of dynamics, objectives, and constraints:

Classical MPC: Continuous or discrete-time optimal control with quadratic or more general stage/terminal costs; efficient solvers for linear systems, more sophisticated for nonlinear/hybrid cases (Bergman et al., 2019, Ghahremani et al., 2021).
Chance-constrained or stochastic MPC: Incorporates probabilistic safety, e.g., collision avoidance under motion or sensing uncertainty using velocity obstacle-based chance constraints, which can be reduced to tractable deterministic forms (Zhang et al., 2021).
Trajectorial/graph-based planners: Discrete graph generation within a rolling local neighborhood, supporting multi-objective (e.g., lexicographic) optimization over risk, comfort, and cost (Shan et al., 2020).
Sampling/tree-based approaches: Tree search (e.g., UCT, CEM) within the receding window, with entire tree reuse for efficiency and improved sample complexity (Lathrop et al., 23 Nov 2024).
Task and motion planning (TAMP) hybrids: Receding-horizon decomposition of combinatorial symbolic-geometric problems, yielding tractable subproblems over sliding windows of actions (Castaman et al., 2020, Braun et al., 2021).
Multi-agent distributed algorithms: Each agent solves its own receding-horizon problem, potentially with fairness- or safety-related consensus constraints solved via distributed optimization methods (Fronda et al., 20 Aug 2025).

This diversity is reflected in domain-specific instantiations, from manipulation in cluttered environments using learned value heuristics (Bejjani et al., 2018), to fair resource scheduling in transportation systems under stochastic uncertainties (Whitaker et al., 7 Aug 2024).

3. Performance Guarantees and Theoretical Properties

Receding-horizon planners can offer strong guarantees when problem structure and constraint formulations are appropriate:

Recursive feasibility: Provided the initial plan is feasible and terminal constraints are properly designed, the rolling process preserves feasibility at each step (Bergman et al., 2019, Ghahremani et al., 2021, Cai et al., 2020).
Stability and convergence: Terminal cost/constraint design ensures Lyapunov descent or cost monotonicity, establishing convergence to desired equilibria or finite-time termination (Bergman et al., 2019, Ghahremani et al., 2021).
Safety and persistent feasibility: RTD (Kousik et al., 2018) guarantees, through offline reachability analysis, that a safe trajectory or braking maneuver is always available under bounded disturbances and sensing limitations.
Regret or risk bounds: Under uncertainty, planner design (e.g., UCB-bandit methods) yields no-regret asymptotics and bounded online performance relative to an oracle (Sun et al., 2016).
Fairness or multi-objective optimality: Lexicographic MPC and distributed schemes accommodate strict priority orderings and resource equity, with explicit optimality or group-level variance constraints (Shan et al., 2020, Fronda et al., 20 Aug 2025, Veer et al., 2022).

However, theoretical guarantees depend sensitively on accurate model knowledge, the choice of horizon length, constraint tightening, and problem regularity.

4. Application Domains and Representative Case Studies

Receding-horizon planners are prominent across domains including:

Application Domain	Core References	Key Features
Multi-agent and multi-vehicle planning	(Zhang et al., 2021, Fronda et al., 20 Aug 2025)	Chance constraints, distributed fairness, collision avoidance
Autonomous ground/aerial robots	(Bergman et al., 2019, Yadav et al., 2022, Wu et al., 2022, Kousik et al., 2018)	Nonlinear dynamics, perception constraints, reachability-based safety
Manipulation in dynamic or cluttered scenes	(Bejjani et al., 2018, Wang et al., 2023, Castaman et al., 2020, Braun et al., 2021)	Online reactivity, learned or relaxed value approximations for hybrid tasks
Scheduling and resource/energy management	(Whitaker et al., 7 Aug 2024)	Hierarchical MILP, stochastic receding-horizon re-planning
Rule/logic-constrained planning	(Veer et al., 2022, Cai et al., 2020)	Rank/differentiable reward preservation, LTL/hard-soft constraint integration
Hybrid and self-adaptive systems	(Ghahremani et al., 2021)	Meta-self-aware hybrid receding-horizon policy switching

For example, in multi-robot systems, distributed receding-horizon fairness planners coordinate energy/resource usage while ensuring safety via barrier function controllers, maintaining real-time feasibility with scaling up to 50 agents (Fronda et al., 20 Aug 2025). In manipulation tasks with dynamic uncertainties, receding-horizon planners leveraging learned value functions achieve robust goal accomplishment and adaptivity in both simulation and real-robot settings (Bejjani et al., 2018, Wang et al., 2023).

5. Extensions: Stochasticity, Fairness, and Hybrid Constraints

Significant advances expand receding-horizon principles to richer settings:

Stochastic uncertainty: Gaussian process modeling of latent dynamics, chance-constrained RHP, and no-regret UCB strategies provide sample-efficient exploration-exploitation and risk control in highly uncertain environments (Sun et al., 2016, Zhang et al., 2021).
Fairness objectives: Recent distributed RHPs explicitly optimize energy or resource variance across agents, often via new consensus-type solvers or penalty terms in horizon-based optimization (Fronda et al., 20 Aug 2025).
Multi-objective/lexicographic priorities: Rule hierarchies (Veer et al., 2022) and lex-MPC (Shan et al., 2020) systematically prioritize safety, regulatory, comfort, and efficiency goals—moving beyond weighted-sum cost structures.
Hybrid symbolic-geometric planning: TAMP methods recast long-horizon, combinatorially complex problems into sequences of receding-horizon geometric subproblems, sometimes aided by problem-specific geometric heuristics or neural value approximators (Castaman et al., 2020, Braun et al., 2021, Wang et al., 2023).
Perception coupling: RHP frameworks account for estimation quality in perception-constrained settings, explicitly optimizing for VIO accuracy or safe tracking in unstructured/feature-sparse environments (Wu et al., 2022).

These extensions position receding-horizon methods as flexible substrates accommodating real-world complexity, including dynamics, logical tasks, sensor/process noise, and team-level performance trade-offs.

6. Computational Considerations and Empirical Performance

Practical deployment of receding-horizon planners leverages methodological innovations for computational tractability and real-time responsiveness:

Problem decomposition: Hierarchical two-stage frameworks (e.g., static reference + rolling local optimization) (Whitaker et al., 7 Aug 2024), system decomposition for reachability (Kousik et al., 2018), and symbolic-geometry hierarchy (Braun et al., 2021) reduce problem size per cycle.
Tree/sample reuse: Model Predictive Trees (MPT) preserve not just the best last plan but entire subtrees for reuse, yielding a 10–20 $\times$ reduction in sample complexity relative to parametric hotstarts (Lathrop et al., 23 Nov 2024).
Warm-start and parallelism: Solvers warm-started with previous horizon solutions or nominal plans achieve per-cycle times of 10–300 ms in settings with up to 50 agents or long manipulation sequences (Bergman et al., 2019, Fronda et al., 20 Aug 2025, Braun et al., 2021).
Closed-form and learning-based surrogates: Minimum-jerk or minimum-snap closed-form generation (Yadav et al., 2022, Wu et al., 2022), and neural oracle value approximators for horizon terminal cost (Wang et al., 2023) enable considerable computational gains (up to 98% online horizon-convergence for humanoid RHP).
Real-world validation: Receding-horizon planners achieve robust execution in fielded mobile robots, industrial disassembly/collaboration, and adversarial or unpredictable context, with demonstrations of strict safety, high mission-completion, and improved resource use (Yadav et al., 2022, Fronda et al., 20 Aug 2025, Lee et al., 2020, Kousik et al., 2018).

A pervasive theme is the tradeoff between horizon length (and model fidelity) and computational delay: short horizons give fast but potentially myopic plans; longer horizons improve performance but risk solve-time overruns and constraint violation in dynamic settings (Bergman et al., 2019, Wang et al., 2023, Lee et al., 2020).

7. Open Problems and Research Directions

Several research frontiers persist:

Unifying multi-scale objectives: Integrating continuous control, discrete task logic, temporal logic, and resource/fairness constraints into a single receding-horizon optimization remains challenging; recent advances in differentiable/relaxable representations show promise (Veer et al., 2022, Cai et al., 2020).
Sample efficiency and learning: Efficient model/data reuse within and across horizon cycles, including contraction-theoretic error accounting and data-driven oracles, can further close the gap to global or long-horizon optimality (Lathrop et al., 23 Nov 2024, Wang et al., 2023).
Scalability to large teams or tasks: Distributed or consensus-based solvers scalable to tens or hundreds of agents with fairness, safety, and dynamic adaptability are an active development (Fronda et al., 20 Aug 2025).
Robustness guarantees under deep uncertainty: Online adaptation to exogenous disturbances, nonstationary or adversarial environments, and real-time safety are increasingly explored via robust RHP, chance constraints, and reachability-based certificates (Zhang et al., 2021, Kousik et al., 2018, Sun et al., 2016).
Perception and task-in-the-loop planning: Incorporating high-level perception and task planning (including hybrid planning meta-self-awareness) into the receding-horizon loop remains an open and fertile research domain (Wu et al., 2022, Ghahremani et al., 2021).

Ongoing work seeks to unify these advances within common computational and theoretical frameworks, supporting rapidly reconfigurable, safe, and mission-optimal behavior in complex, uncertain, and collaborative settings.