Temporal Cascading of Planning and Control for Quadrotor MPC

arXiv:2512.12427 · cs.RO, cs.SY, eess.SY · Submitted 2025-12-13 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: I'm Rosa, and with me are Dev and Taro, guest researcher.

Dev: Today's paper: "Temporal Cascading of Planning and Control for Quadrotor MPC".

Rosa: Many aerial tasks involving quadrotors demand both instant reactivity and long-horizon planning for obstacle avoidance, energy efficiency, or trajectory tracking.

Dev: First, who's behind it and why it matters.

Title and authors: Rosa: Well, Dev, Taro, this paper titled "Temporal Cascading of Planning and Control for Quadrotor MPC" is pretty interesting because it tackles that classic problem of needing both fast reactions and long-term planning for aerial robots.

Dev: I agree, Rosa; the core idea seems to be addressing the limitations of current hierarchical setups where planners use simple models and controllers use complex ones, which naturally leads to suboptimality.

Taro: That's exactly what I was thinking; traditional decomposition means the controller is just limited by whatever coarse plan it gets from the planner, which isn't ideal for dynamic situations.

Rosa: So, what does this UNIQUE architecture actually propose in terms of how it structures this planning and control relationship?

Dev: It suggests replacing that separate planning stage entirely with a temporal cascading structure inside one single MPC optimization problem.

Taro: That sounds like a significant structural change; instead of two separate loops, you’re embedding the long-horizon planning as the second tail horizon of a multi-phase MPC formulation.

Rosa: The paper claims they formulate the planning problem as this second tail horizon rather than solving it in isolation, which is quite different from how things are usually done.

Dev: They also focus on aligning costs across these different horizons and deriving feasibility constraints specifically for the point-mass planning model to ensure compatibility with the high-fidelity actuator limits.

Taro: I noticed they introduce transition constraints that link the high-fidelity states to meaningful low-fidelity states, which seems like a smart way to bridge that fidelity gap between models.

Rosa: And how do they handle the computational challenges of solving this large optimization problem in real time?

Dev: They use parallel point-mass and mixed-integer solvers to handle those nonconvexities, and they also incorporate progressive three dee obstacle smoothing over the planning horizon to improve convergence speed.

Taro: That parallel re-planning strategy sounds like it’s a key piece for robustness; I wonder how much benefit that actually gives when things in the environment misbehave unexpectedly.

Title and authors: Rosa: The results they show under equal computational budgets are quite compelling, suggesting this architecture improves closed-loop tracking by up to seventy-five percent compared to standard MPC and hierarchical baselines.

Dev: That improvement figure is substantial, Rosa; it really shows the benefit of aligning the objectives across both horizons within that single optimization framework.

Taro: If we look at what they did for the world misbehaving, the paper mentions that this two-phase formulation converges well around local minima, but they also propose a parallel computation strategy to tackle those severe nonconvexities when planning involves complex maneuvers.

Rosa: So, to summarize the main idea of "Temporal Cascading of Planning and Control for Quadrotor MPC," it’s unifying planning and control into a single optimization by making the planning problem the second tail horizon of an MPC, which they do by aligning costs and using transition constraints to link high-fidelity states to low-fidelity states.

Dev: That unification allows the controller to optimize a consistent objective across both horizons simultaneously, which is something conventional hierarchical stacks struggle with because the controller only sees a coarse plan.

Taro: The way they derive feasibility constraints for the point-mass model and use progressive smoothing to improve numerical robustness over long horizons with sharp geometry seems like a practical step toward making this work in real-world, cluttered environments where those geometric details matter.

Rosa: So, moving on to the specific improvements they suggest, it seems their main contribution is really shifting the planning paradigm from a hierarchical stack to this temporal cascading structure within one optimization framework.

Dev: They also provide a two-phase MPC architecture specifically tailored for quadrotors, coupling the high-fidelity model with a long-horizon point-mass model using equality constraints on position and velocity, thrust-induced acceleration, and jerk/body-rate mappings.

Taro: Those coupling constraints are crucial because they ensure that the fast dynamics of the quadrotor are respected while still allowing for the slower, more strategic planning provided by that point-mass model.

Rosa: They also developed feasibility-preserving low-fidelity constraints for the point-mass model and used parallel tail-horizon re-planning to compare alternative solutions from randomly initialized solvers.

Title and authors: Dev: Those approximations help ensure numerical robustness over long horizons with sharp geometry, and the parallel computation strategy really helps in finding better solutions when the planning problems have severe nonconvexities.

Taro: When we consider what this means for the world misbehaving, their ability to handle severe nonconvexities through parallel re-planning suggests a much better chance of finding viable trajectories even when local minima are present during long-horizon planning.

Rosa: So, in conclusion for "Temporal Cascading of Planning and Control for Quadrotor MPC," the paper demonstrates that treating planning as a tail-horizon problem within an MPC, coupled with alignment across horizons and parallel re-planning, leads to superior closed-loop performance compared to standard MPC and hierarchical designs.

Dev: The implication here is that we can achieve better long-term trajectory tracking and obstacle avoidance in aerial systems without having to drastically shorten the horizon of the main control loop just to keep things real time feasible.

Taro: For autonomy, this suggests that AI agents can maintain a much more robust strategic plan over extended periods, even when faced with unexpected environmental disturbances because they are constantly re-evaluating potential future paths in parallel.

Rosa: This work is really pushing the boundary on how we balance the need for immediate reactivity with necessary long-term strategy in aerial robotics, and I'm excited to hear what these results mean for real deployments outside of a controlled lab setting.

Dev: If this works outside the lab, that means we could see much more reliable performance in complex, dynamic environments where those traditional cascaded systems usually fall apart.

Taro: It points toward an AI system capable of truly strategic navigation, not just reactive obstacle avoidance; it’s about planning for the mission goal while keeping immediate safety constraints firmly in mind.

Rosa: That's what I wanted to hear; moving from just reacting to obstacles to actually navigating a complex space intelligently using this unified MPC approach is a big step forward for field robotics.

The paper's summary: Rosa: So, to recap, this paper proposes changing how we think about aerial robotics control by embedding long-horizon planning as a second tail horizon within a single Model Predictive Control optimization problem instead of using separate planning and control loops.

Dev: That’s right; it moves the whole process from a sequential hierarchy to something more integrated. The main takeaway is that they align the costs across both horizons, which means the controller isn't optimizing for a plan that might be instantly invalidated by physical constraints in the next moment.

Taro: From an autonomy research standpoint, this integration means if we have a long-term goal, like navigating around a massive obstacle field, the immediate control actions are already informed by that larger strategy. It’s about achieving better trajectory tracking over extended periods because the planning isn't just a guess followed by correction.

Rosa: Exactly; they show that when you combine this unified MPC approach with parallel re-planning strategies, you get significantly better closed-loop performance, up to seventy-five percent improvement in cost compared to standard methods under the same computational budget. That’s substantial data for field robotics.

Dev: The real win for me is the latency and stability aspect; they show that this integrated framework can handle long-horizon reasoning—like planning over forty meters—while keeping iteration times well under five milliseconds, which is what we need for a stable control loop. It bypasses the issue where high-fidelity models force us to cut the horizon down just to stay real time feasible.

Taro: I’m particularly interested in how it handles when the environment gets messy; they use those parallel point-mass solvers against random initializations of alternative solutions, which seems designed specifically to prevent getting stuck in poor local minima during long-range planning maneuvers. That robustness is what we need for unpredictable real-world scenarios.

Rosa: It really suggests that this isn't just theoretical; the paper’s evaluation in simulation and real flights shows these gains hold up, even when comparing it against those traditional hierarchical baselines where the controller is limited by a much coarser plan. But I gotta ask, Dev, how long can we expect these results to hold up once we move it fully off the lab bench and into a genuinely cluttered environment?

Dev: That’s a fair question, Rosa; the authors tested it in real flights and showed substantial gains even there. The point is that they’ve engineered the constraints—the way they map high-fidelity states to low-fidelity states via those transition constraints—to be robust enough for the actual actuator limits we see in the field. It moves away from relying on overly conservative, simplified geometric models that often plague hierarchical setups.

Taro: And that mapping is key; it lets us leverage the speed of the point-mass model for planning without losing the precision needed for high-fidelity control during execution. This dual approach seems to be exactly what’s needed to make autonomous systems truly agile in complex settings.

Rosa: It sounds like this paper is pushing us toward a new way of designing aerial AI systems where strategic mission objectives and immediate safety constraints are optimized together, rather than being handled as separate stages. So, we’ve seen the core concept and the impressive performance metrics. Now let’s look at those specific technical contributions—how exactly did they manage those transition constraints to bridge that fidelity gap?

The paper's improvements: Rosa: So, to wrap up on their technical improvements, the paper highlights several mechanisms they introduced to make this temporal cascading structure actually work reliably in practice.

Dev: They focused heavily on deriving feasibility-preserving low-fidelity constraints for that point-mass model; that part ensures that even when we simplify the planning model for speed, those simplified plans still respect the physical limitations of the high-fidelity quadrotor actuators and rate limits.

Taro: And they tackled numerical stability over long prediction horizons by adapting progressive three dee obstacle smoothing; this morphing of cube-like sets into ellipsoids as the prediction time increases is a smart way to make those long plans computationally tractable without losing too much spatial accuracy.

Rosa: That smoothing technique sounds like it directly addresses the issue we had with sharp geometry causing convergence problems in longer simulations, which makes me think about how this applies to real-world sensor noise and measurement uncertainty.

Dev: It’s more than just smoothing; it’s a way to morph the problem space progressively so that the solver doesn't have to tackle the most complex geometry right away when it first starts planning, which keeps the iteration times low throughout the entire process.

Taro: That progressive approach is also tied into their parallel tail-horizon re-planning strategy; this allows for a kind of safety net where if one path looks bad, they can quickly test alternative solutions generated by different point-mass solvers without having to restart the whole heavy optimization from scratch.

Rosa: It sounds like they’ve built a system that is not only faster but also much more resilient when the environment throws curveballs at it, which is exactly what we need for field robotics where things rarely go perfectly according to simulation.

Dev: The implication here for control engineering is that we can design systems where the planning stage doesn't become a bottleneck; because they handle the long-horizon work in parallel or via simplified models, the actual flight controller gets to focus on maintaining high-frequency stability and latency targets.

Taro: If this framework scales well to handle large mazes with many obstacles, as suggested by their evaluation, it opens up possibilities for swarm robotics where individual agents can coordinate long-term navigation paths efficiently while still reacting instantly to local threats.

Rosa: It really does look like a system that moves us closer to building autonomous aerial agents capable of complex mission execution over extended periods in genuinely unstructured spaces. But I still have my main question: how far out are these real-world performance claims? Are we talking about sustained flight for hours, or just short, high-stakes maneuvers?

Conclusion: Rosa: So we’ve covered a lot on the "Temporal Cascading of Planning and Control for Quadrotor MPC" paper, and to recap, the authors successfully unified long-horizon planning and immediate control into a single optimization problem by embedding planning as a tail horizon.

Dev: That's right; it fundamentally changed how we structure the control loop by aligning objectives across those horizons, which gives us better consistency in performance under dynamic conditions.

Taro: I still think the most exciting part is that their method for handling world misbehavior, specifically using parallel re-planning against random initializations, shows a much stronger ability to recover from local minima during long-horizon planning than what we’ve seen before.

Rosa: It really does suggest we can move toward autonomous systems that maintain strategic goals over extended durations without sacrificing immediate safety or reactivity. But I still have my main question for you, Dev; how far out are these real-world performance claims? Are we talking about sustained flight for hours, or just short, high-stakes maneuvers?

Dev: The authors tested it in real flights and showed substantial gains even there, Rosa; the point is that they’ve engineered the constraints—the way they map high-fidelity states to low-fidelity states via those transition constraints—to be robust enough for the actual actuator limits we see in the field. It moves away from relying on overly conservative, simplified geometric models that often plague hierarchical setups.

Taro: That mapping is key; it lets us leverage the speed of the point-mass model for planning without losing the precision needed for high-fidelity control during execution. This dual approach seems to be exactly what’s needed to make autonomous systems truly agile in complex settings.

Rosa: It sounds like this paper is pushing us toward a new way of designing aerial AI systems where strategic mission objectives and immediate safety constraints are optimized together, rather than being handled as separate stages. But I still have my main question for you, Dev; how far out are these real-world performance claims? Are we talking about sustained flight for hours, or just short, high-stakes maneuvers?

Wrap-up: Dev: The authors showed significant gains in closed-loop tracking even in real flights when compared to hierarchical baselines, Rosa; the point is that they’ve engineered the constraints—the way they map high-fidelity states to low-fidelity states via those transition constraints—to be robust enough for the actual actuator limits we see in the field. It moves away from relying on overly conservative, simplified geometric models that often plague hierarchical setups.

Rosa: It really does look like a system that moves us closer to building autonomous aerial agents capable of complex mission execution over extended periods in genuinely unstructured spaces. But I still have my main question for you, Dev; how far out are these real-world performance claims? Are we talking about sustained flight for hours, or just short, high-stakes maneuvers?

Dev: They did show substantial gains in closed-loop tracking even in real flights when compared to hierarchical baselines, Rosa; the point is that they’ve engineered the constraints—the way they map high-fidelity states to low-fidelity states via those transition constraints—to be robust enough for the actual actuator limits we see in the field. It moves away from relying on overly conservative, simplified geometric models that often plague hierarchical setups.

Wrap-up: Taro: That mapping is key; it lets us leverage the speed of the point-mass model for planning without losing the precision needed for high-fidelity control during execution. This dual approach seems to be exactly what’s needed to make autonomous systems truly agile in complex settings.

Rosa: It really does look like a system that moves us closer to building autonomous aerial agents capable of complex mission execution over extended periods in genuinely unstructured spaces. But I still have my main question for you, Dev; how far out are these real-world performance claims? Are we talking about sustained flight for hours, or just short, high-stakes maneuvers?

Rudolf Reiter, Chao Qin, Leonard Bauersfeld, Davide Scaramuzza

University of Zurich

cs.RO, cs.SY, eess.SY

Submitted: 2025-12-13

Updated: 2026-09-29

Journal ref: IEEE Transactions on Robotics 2026

DOI: 10.1109/TRO.2026.3726670

Code: https://github.com/betaflight/betaflight

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 90/100

The gist: Many aerial tasks involving quadrotors demand both instant reactivity and long-horizon planning for obstacle avoidance, energy efficiency, or trajectory tracking.

Key concepts

Temporal Cascading: This architecture replaces separate planning and control loops with a single Model Predictive Control optimization problem. It embeds the long-horizon planning as the second tail horizon, ensuring that the controller optimizes a consistent objective across both fast and slow time scales.
Transition Constraints: These constraints link high-fidelity states of the quadrotor to meaningful low-fidelity states used in planning. They are crucial for bridging the gap between complex physical dynamics and simplified planning models, ensuring feasibility while respecting actuator limits.
Parallel Re-planning Strategy: This strategy uses parallel point-mass solvers against random initializations of alternative solutions. It helps the system handle severe nonconvexities and local minima during long-range planning maneuvers, increasing robustness when the environment is unpredictable.
Progressive Three Dee Obstacle Smoothing: This technique morphs cube-like sets into ellipsoids as the prediction time increases. This makes long plans computationally tractable by progressively simplifying complex geometry, which improves numerical stability over long horizons.

Terminology

Fidelity — 165× in this paper · explained in 2 episodes
Alignment — 11× in this paper · explained in 1 episode
Robustness — 7× in this paper · explained in 5 episodes
Accuracy — 6× in this paper · explained in 1 episode
Benchmark — 4× in this paper · explained in 2 episodes
Consistency — 4× in this paper · explained in 3 episodes
Ablation — 3× in this paper · explained in 1 episode
Core — 3× in this paper · explained in 2 episodes
Energy Efficiency — 3× in this paper · explained in 3 episodes
Pruning — 3× in this paper · explained in 4 episodes
Reinforcement Learning — 3× in this paper · explained in 4 episodes
Adaptation — 2× in this paper · explained in 1 episode
Hierarchical Framework — 2× in this paper · explained in 2 episodes
AI Agents — 1× in this paper · explained in 2 episodes
Abundance — 1× in this paper · explained in 1 episode
Actor — 1× in this paper · explained in 3 episodes
Decoupling — 1× in this paper · explained in 2 episodes
Local Optimization — 1× in this paper · explained in 2 episodes
Loss Function — 1× in this paper · explained in 2 episodes
Model Predictive Control (MPC) — 1× in this paper · explained in 5 episodes
Physical Constraints — 1× in this paper · explained in 7 episodes
Redundancy — 1× in this paper · explained in 2 episodes

Summary

Many aerial tasks involving quadrotors demand both instant reactivity and long-horizon planning for obstacle avoidance, energy efficiency, or trajectory tracking. High-fidelity models enable accurate control but are too slow for long horizons; low-fidelity planners scale but cannot control the system directly, necessitating cascaded architectures. Prevailing hierarchical approaches plan with a simplified model and use a high-fidelity controller for tracking, yet this decomposition is inherently suboptimal. The controller is limited by the coarse plan, and conventional MPC alternatives shorten the horizon to stay real-time feasible.

We present UNIQUE, an MPC architecture that replaces this hierarchical stacking with temporal cascading. The planning problem is formulated as the second tail horizon of a single multi-phase MPC, rather than solved separately. We align costs across horizons, derive feasibility constraints for the point-mass planning model, and introduce transition constraints that convert high-fidelity states into meaningful low-fidelity states. Parallel point-mass and mixed-integer solvers address nonconvexities while incorporating progressive 3D obstacle smoothing over the planning horizon. In simulation and real flights, under equal computational budgets, UNIQUE improves closed-loop tracking by up to 75% compared with standard MPC and hierarchical baselines.

Our pivotal idea is to replace the conventional hierarchical planner-controller decomposition with a temporal cascading of planning and control inside a single MPC. Rather than computing a plan separately and tracking it, we embed the planning problem as the second tail horizon of a multi-phase MPC, as sketched in Fig. 1. This is motivated by the fact that an MPC, in general, aims to optimize the same underlying task objective and aims to satisfy the same constraints as the planning problem. We observe that (i) geometric planning around obstacles is predominantly a long-horizon problem with negligible influence on the short control horizon, and (ii) a point-mass planner can be solved very fast within each closed-loop iteration. Therefore, we formulate the planning problem as finding the optimal tail trajectory on the second horizon, given that we can effectively convert high-fidelity states into meaningful low-fidelity states and map constraints from the high- to the low-fidelity model, which we show to be possible for quadrotors. The two phases are coupled by transition constraints that align (i) position and velocity, (ii) thrust-induced acceleration, and (iii) jerk/body-rate relations. Cost terms are aligned across horizons, allowing the controller to optimize a consistent objective. To improve numerical robustness over long horizons with sharp geometry, we adapt progressive smoothing [6] of norm-based obstacle models for 3D shapes, morphing cube-like sets to ellipsoids with increasing prediction time, which improves real time iteration (RTI) convergence [7].

Our contributions are as follows:

** Temporal planning paradigm. We propose to formulate the planning problem not hierarchically but as the tail horizon of an MPC, yielding a sequential controller-planner structure within a single optimization.**

** Two-phase MPC architecture for quadrotors. A single optimization that couples a high-fidelity quadrotor model with a long-horizon point-mass model via equality constraints on position/velocity, thrust-acceleration, and jerkbody-rate mappings, with cost alignment across horizons.**

** Feasibility-preserving low-fidelity constraints. Derivation and tractable inner approximations of thrust and body-rate safe sets for the point-mass model that ensure compatibility with high-fidelity actuator and rate limits.**

** Parallel tail-horizon re-planning. A parallel computation strategy that compares the tail trajectory of the main MPC against alternative solutions from randomly initialized point-mass solvers.**

** Pareto-superior control performance. Under equal computational budgets, the two-phase formulation achieves better closed-loop performance than extending the highfidelity MPC horizon.**

** Comprehensive evaluation. Simulations and real flights show substantial closed-loop gains over standard MPC and hierarchical baselines under equal compute budgets, including Pareto analyses across horizon variations and feasibility approximations, as well as demonstrations of long-horizon planning with iteration times below 5 ms.**

The UNIQUE framework lowers the planning-control performance gap by treating planning as a tail-horizon problem of MPC rather than a separate hierarchical stage. In obstaclerich tasks, we observe up to 75% lower closed-loop cost compared to standard MPC and hierarchical designs, while reducing online computation compared to long-horizon, highfidelity MPC.

The complete UNIQUE algorithm is stated in Alg. 1. We use the notation Ik = k, k + 1,..., N + M + 1 for the prediction indexes of the MPC. In order to solve (21) numerically efficiently, we use the solver ACADOS [38] with the interior-point quadratic program (QP) solver HPIPM [39] without condensing, and deploy the RTI scheme [7]. We do not use condensing, since for the considered problem size we did not observe an improvement.

Improvements for AI systems

As a fastidious and diligent researcher, I have analyzed the Temporal Cascading of Planning and Control for Quadrotor MPC paper by Reiter et al. The core innovation is replacing hierarchical planning with a unified, multi-phase Model Predictive Control (MPC) framework where long-horizon planning is embedded as the second tail horizon of the main optimization.

Here are specific improvements to AI systems that can be made by implementing the UNIQUE framework, and what these improved systems can do:

Based on the UNIQUE framework, AI systems (specifically autonomous aerial agents like quadrotors) will gain significant capabilities in complex, dynamic environments by achieving a superior balance between long-term strategic planning and real-time reactive control.

Here are the specific improvements:

mathbfSuperior Closed-Loop Performance in Cluttered/Obstacle-Rich Environments:

The system can achieve up to 75% lower closed-loop cost compared to standard MPC and hierarchical baselines, especially when navigating environments with numerous local minima (e.g., dense mazes).

mathbfEnhanced Robustness Against Local Minima Traps:

By employing a parallel re-planning strategy (comparing the main MPC's tail trajectory against alternative solutions from randomly initialized point-mass solvers) and utilizing progressive obstacle smoothing, the system is significantly less likely to get stuck in suboptimal local minima during long-horizon planning.

mathbfReduced Computational Overhead for Long-Horizon Planning:

The system avoids the need for separate, slow hierarchical planners by formulating geometric planning as a second horizon within a single NLP. This allows for long-horizon reasoning (obstacle avoidance, energy efficiency) to be performed in real time (with iteration times below 5ms), unlike high-fidelity MPC which must shorten its horizon to remain feasible.

mathbf Seamless Integration of High-Fidelity Control and Low-Fidelity Planning:

The system couples a high-fidelity quadrotor model (for precise control) with a low-fidelity point-mass model (for fast, long-horizon planning) through carefully derived transition constraints (position/velocity alignment, thrust/acceleration mapping). This eliminates the suboptimal coupling issues inherent in traditional hierarchical stacks.

mathbf Improved Constraint Handling via Approximation:

The framework allows for the use of tractable inner approximations for non-linear constraints (e.g., progressive smoothing of obstacle shapes and simplified box/polyhedral constraints on low-fidelity states), ensuring numerical robustness over long horizons without requiring overly conservative geometric models that slow down computation unnecessarily.

mathbf Adaptive Computational Efficiency:

The system can dynamically manage computational load by offloading the combinatorial search for better long-term trajectories to parallel, asynchronous solvers (like MIQP or point-mass planners). The main control loop remains fast, while the complex planning search runs concurrently, ensuring the real-time control loop is never blocked.

Based on these improvements, an AI system utilizing this UNIQUE framework can perform:

mathbf Agile and Precise Navigation in Complex Scenarios:

The system can track periodic trajectories (e.g., figure-eights) while navigating dense obstacle fields with high accuracy (achieving tracking errors up to 0.8m on tight turns), which is difficult for hierarchical approaches that rely on conservative point-mass models.

mathbf Efficient, Long-Horizon Mission Planning:

The system can plan optimal paths over long durations (e.g., traversing a 40m tunnel) while simultaneously ensuring immediate obstacle avoidance and adherence to strict dynamic constraints (like maximum thrust limits), leading to better energy efficiency than standard MPC extensions that simply increase the horizon length.

mathbf Real-Time Decision Making Under High Dynamics:

The system can maintain stable flight dynamics in highly dynamic, non-smooth environments (e.g., suddenly appearing objects) by leveraging the rapid reinitialization strategy, allowing it to adapt its long-term plan quickly when a local minimum is encountered.

mathbf Scalable Obstacle Avoidance for Large Environments:

The system can handle large mazes with many obstacles (up to 50 in simulation) without computational time scaling prohibitively, thanks to the pruning and preprocessing strategies within the mixed-integer planner component.

Sources

Rollout Then Optimize: A One-Step Newton Refinement of Learned Policies for Nonlinear Model Predictive Control