Quadrotor Control

As modern societies rely more on autonomous systems to facilitate daily life, assuring their safe operation is paramount. Naturally, there are many techniques available to predict and prevent system failures. However, the safety afforded by such schemes may become misaligned with the true system, which can change in unexpected ways - from partial faults to natural wear-and-tear - that subtly degrade its stability. The implications that such subtle changes have on autonomous system stability can be observed through generic indicators of resilience derived from critical slowing down, popular for anticipating catastrophic tipping points in natural systems. Here, we show how one can systematically design these generic indicators for nonlinear control systems and show how these can reflect loss of stability though simulations of canonical robotic systems wherein their proximity to instability is manipulated directly. These results are affirmed through real-world flight experiments of a quadrotor that is nudged towards instability by progressively damaging its propeller blades. Our results show that the implications of degraded resilience on closed-loop stability are evident well before they appear, for which the indicators of resilience derived here can provide an early warning.

Deep Reinforcement Learning has demonstrated remarkable capability in quadrotor control, yet learned policies offer no guarantee of respecting safety constraints during training or deployment. We present CALOS (Control-Affine Lyapunov On-manifold Safety), a runtime safety layer that enforces attitude constraints on a quadrotor without modifying the underlying learning algorithm. CALOS formulates four tilt-angle inequalities and a Lyapunov descent condition as a single quadratic program whose solution is the minimum-norm correction to the nominal torque output of the policy. The quadratic program is solved exactly via active-set enumeration over the three-dimensional torque space, with a computational cost low enough to enforce constraints in real time across thousands of parallel simulation environments, as required by modern massively parallel Deep Reinforcement Learning training. Evaluated on trajectory-tracking tasks in NVIDIA Isaac Lab, CALOS reduces lateral tracking error by 55-60% relative to an unconstrained Proximal Policy Optimization baseline while achieving zero attitude-constraint violations on the training trajectory. By restricting exploration to safe regions of the state space, the safety layer also accelerates training convergence and improves data efficiency without producing suboptimal policies.

Combining aerial thrust with spring-loaded hopping makes monopedal quadcopters promising for locomotion over complex terrain, but heuristic proportional-integral-derivative (PID) tuning limits coordination between active thrust and passive contact dynamics. We present a direct estimated-state-to-motor Proximal Policy Optimization (PPO) policy that commands four motors without an explicit hopping state machine or low-level attitude PID. Its reward combines Energy-Manifold Shaping for mass-normalized vertical-energy tracking and apex-state anchoring with Efficiency Shaping, which uses a history-aware power estimator to penalize general power use, impose an additional airborne-power cost, and penalize airborne near-stationarity. In representative hardware runs, the PPO-based control stack reduced cycle-averaged measured electrical power by 30.7% and mean total normalized thrust by 49.8% relative to the tuned PID-based control stack, while retaining repeatable commanded-height hopping and more concentrated landings. These observations are consistent with improved use of passive dynamics and reduced measured electrical demand.

Although aerial-legged robots offer combined agility and efficiency, controlling high-speed hopping under complex hybrid dynamics is challenging. Reinforcement Learning (RL) is promising but prone to energy-inefficient "reward hacking". We propose a Dynamics-Informed RL framework for a monopedal hopping quadcopter. By embedding a target Specific Energy into the reward, we constrain the optimization to a physically viable energy manifold, ensuring stable hopping behaviour. By rewarding the phase-consistent behavior, it can encourage bio-inspired stance-phase impulse. Furthermore, penalizing the electro-mechanical power waste induces the motors generate an efficient impulse. This enables the policy to inject energy strictly during spring restitution without heuristic state machines. MuJoCo simulations validate robust height regulation and forward velocity tracking up to 2.0 m/s despite severe attitude-contact coupling. Ultimately, our approach yields a highly agile hopping gait, reducing energy consumption by 82% and 73% compared to hovering baselines and inefficiency baseline, respectively.

Recovering unmanned aerial vehicles (UAVs) in maritime environments is challenging due to wind turbulence and ship-deck motion, making it a valuable test case for alternative control and learning approaches as conventional landing approaches often become unreliable. We study simulated mid-air capture of quadrotor UAVs by a ship-mounted robotic arm, learning robust cooperative control policies with Heterogeneous-Agent Proximal Policy Optimization (HAPPO) Reinforcement Learning. We train with HAPPO using a curriculum and an adversarial wind agent (HARL-AC) in NVIDIA Isaac Lab, and compare the obtained control policies against those generated through curriculum-based domain randomization and a benchmark trained on a single sea state. In-distribution evaluation on sea states $0/4/5$ shows comparable success for HARL-AC and domain randomization of up to $97.5\%$. On out-of-distribution sea states $7/8/10$, HARL-AC generalizes better, achieving up to $16\%$ higher median success rate at sea state 10, and substantially lower crash rates of up to $14\%$ compared to the domain randomization policy. Furthermore, we show that the adversarially trained policy shows more cautious behavior, slightly increasing timeouts by $<3\%$, but yields safer recovery behavior in severe, unseen conditions.

Accurate dynamic models play a central role in achieving reliable control of quadcopters. Classical system identification methods remain widely used, mainly because of their interpretability. However, they often fail to capture important nonlinear effects, especially in small-scale aerial platforms where such effects become more pronounced. Data-driven approaches offer a different perspective. They can represent complex nonlinear dynamics more effectively, but this comes at the cost of reduced interpretability and the absence of well-calibrated uncertainty estimates. In this work, we propose a framework that combines physics-based modeling with data-driven learning, while explicitly accounting for uncertainty. A physics-based model is first identified using the Prediction Error Method (PEM), which captures the main structure of the system. The remaining dynamics are then modeled using a Gaussian Process (GP), allowing the residual behavior to be learned directly from data. This separation makes it possible to distinguish between known physical effects and unmodeled dynamics. The proposed framework is validated on a Duckiedrone-like experimental setup. The results show that the PEM-GP model achieves prediction accuracy comparable to that of a Long Short-Term Memory (LSTM) network, while additionally providing calibrated uncertainty estimates. This combination improves model reliability and supports uncertainty-aware decision-making.

Modern stochastic predictors can model rich, multi-modal outcome distributions. However, this expressive power comes with challenges in ensuring robust predictions $-$ a critical requirement in safety-critical domains. Randomized smoothing is a leading technique for improving robustness, particularly against adversarial perturbations. Yet, in stochastic multi-modal regression settings, randomized smoothing often fails due to mode collapse, yielding averaged predictions that do not reflect the underlying distribution. To address this limitation, we propose clustered $α$-smoothing, a framework that (1) partitions noisy samples using an arbitrary clustering algorithm, (2) applies $α$-smoothing locally within each cluster, and (3) combines the resulting predictions into a mixture distribution. By interpreting the smoothing distribution as a mixture of $α$-smoothers, we derive a lower bound on the probability that the smoothed prediction lies within a union of compact regions corresponding to distinct modes. We empirically evaluate our framework on two benchmarks, demonstrating substantial improvements over state-of-the-art methods. In stochastic trajectory prediction on a driving simulator dataset, our approach achieves, on average, a $27\%$ lower Wasserstein distance to the ground-truth distribution compared to $α$-smoothing. In quadrotor control, where modes correspond to distinct feasible paths to a target, our method reduces the collision rate by $81\%$ relative to the state-of-the-art randomized smoothing.

Digital-twin calibration requires interaction data that is expensive to collect. We study two acquisition decisions: which trajectories to generate, and when to spend a limited budget on privileged parameter measurements. Our framework couples an excitation-oriented reinforcement learning controller, a recurrent parameter estimator with predictive uncertainty, and a budgeted query policy. In Pendulum, a Random Forest diagnostic recovers gravity only weakly from task-oriented trajectories and does not recover mass or length, while a GRU trained on excitation-oriented trajectories reaches a mean absolute error of 0.0066 with no queries. We then withdraw continuous oracle access partway through an episode, so that the twin must run on the estimator's output for the remainder. The estimator-plus-policy pipeline achieves a terminal error of 0.0092 under a three-query budget, against 0.2031 for an uncalibrated twin. In partially observable Waterworld, five controllers produce different observed error profiles across three hidden parameters, and an estimator trained on a five-controller mixture reaches online normalized errors of roughly 4-5%. These exploratory case studies are not controlled ablations, but they motivate treating trajectory design and query allocation as explicit design variables in data-scarce calibration.

Unmanned aerial vehicles (UAVs), particularly quadcopters, present unique challenges for autonomous control due to their underactuated dynamics: only four available control inputs must govern six degrees of freedom. This paper investigates a physics-aware, end-to-end deep reinforcement learning (DRL) approach that acts directly on low-level body inputs, total thrust and body torques $(T, τ_x, τ_y, τ_z)$, and closes the loop through a high-fidelity Simulink environment. Our simulator integrates a 12-state rigid-body model (MATLAB Level-2 S-Function) with (i) an Action2RPM allocation based on the Moore-Penrose pseudo-inverse of a coefficient matrix derived from thrust and drag terms, and (ii) first-order actuator dynamics for each motor (time constant $T_m = 0.076$ s), including rotor gyroscopic coupling. A shaped reward balances goal-reaching and stability using an exponential position well, attitude penalties, and quadratic velocity costs. Four DRL algorithms, DDPG, TD3, PPO, and SAC, are evaluated in two stages: (S1) thrust-only hover and (S2) hover with pitch torque and a translated goal. Results show that SAC and TD3 achieve superior stability and exploration efficiency, while PPO is less sample-efficient. The study highlights the significance of modeling actuator lags and aerodynamic moments for stable low-level control and provides a reproducible benchmark for quadcopter DRL.

We develop a novel forecasting scheme to anticipate controller induced loss of control (LOC) in quadrotors and evaluate it on real LOC flight data from four different quadrotors. For this, early warning signals of LOC are derived using critical slowing down (CSD), a generic phenomenon shown to precede critical transitions across various complex ecological and biological systems. As such, our early warning indicators are generic in the sense that no system models are needed to facilitate forecasts of LOC. The approach is evaluated on real quadrotor flight data wherein LOC occurs due to unstable controller behavior arising from input-output delays. Our approach achieves a time-to-LOC forecast of up to 0.9 seconds before LOC occurs, outperforming state-of-the-art recurrent neural network quadrotor LOC forecasters in terms of detection accuracy and LOC data reliance. In particular, we leverage insights from CSD to accurately predict LOC without using data of the LOC event itself. Going further, we apply our forecasters without any re-parameterization to anticipate a different LOC scenario, quadrotor flyways, that occur on other quadrotors flying both indoors and outdoors. Despite these differences, our approach successfully detects LOC, demonstrating that it can generalize across controller architectures, quadrotors, and LOC scenarios.

Incremental Nonlinear Dynamic Inversion (INDI) is attractive for unmanned aerial vehicle (UAV) flight control because it reduces dependence on a full aerodynamic model while retaining strong disturbance-rejection capability. For a tilt-rotor vertical takeoff and landing (VTOL) architecture, however, the admissible model-mismatch range of the fast inner loop is still not characterized analytically in a parameter-explicit way. This paper isolates the pitch-rate/elevon subchannel of an existing cascaded INDI controller and studies its linear stability under model mismatch. A closed-form fifth-order transfer function is derived for the full controller-estimator-actuator-plant interconnection, and stability is characterized through the Routh-Hurwitz criterion over a parameterized linear model. Two representative three-parameter sweeps produce interpretable stability regions. Based on these feasibility maps, two uncertainty-aware tuning procedures are proposed: a robustness-oriented design that maximizes a weighted worst-case combination of gain margin and phase margin, and a performance-oriented design that maximizes worst-case closed-loop bandwidth subject to margin constraints. The results show that actuator lag and inertia mismatch are comparatively benign at nominal gain, whereas control-effectiveness mismatch, particularly a sign error in the allocation, is the most dangerous destabilizing factor, leading to concrete tuning recommendations for conservative and aggressive operating conditions.

We investigate conditional invertible neural networks (cINNs) as probabilistic inverse-dynamics models for multirotor control. For a planar X8 coaxial multicopter, we learn $p(u \mid s_t, c_t)$ from an incremental nonlinear dynamic inversion (INDI) teacher using rational-quadratic spline coupling and invertible linear mixing. Open-loop reproduction reaches $R^2 = 0.944$, mean CRPS 0.0915, and log-probability-error correlation $ρ= -0.60$. Over 15 closed-loop scenarios, position RMSE matches INDI (9.7 vs. 9.5 m), with 47 percent tracking acceptably; failures separate into attitude divergence under aggressive steps and phase lag under high-frequency references, isolating command bandwidth and data coverage as dominant failure mechanisms.

Quadrotors flying in tight formations are severely affected by turbulent aerodynamic interactions, such as downwash, that can cause catastrophic collisions if left unmodeled. To compensate for these effects, we propose a physics-informed residual dynamics learning framework that captures complex aerodynamic interactions while ensuring the joint multi-quadrotor system remains differentially flat. We leverage this preserved flatness to design a computationally efficient feedback linearization controller that is easily tunable with linear control techniques and cancels aerodynamic disturbances via feedforward compensation. Hardware experiments demonstrate our framework reduces average tracking errors by 31% compared to nominal baselines. Crucially, our lightweight approach matches the tracking performance of state-of-the-art nonlinear model predictive control (NMPC) while requiring an order of magnitude less computation. We are the first to show that stable, tight formation flight can be achieved with under 30 seconds of training data and a 5ms loop rate, unlocking high-fidelity aerodynamic compensation for compute-constrained flight stacks.

A method for the control of quadrotors is presented. It is composed of a high-level reference smoothing step and a low-level reference tracking step. The high-level step leverages the Dubins airplane model for dimensionality reduction and reduced computational complexity, and exploits its structure for decoupling, spatial modeling and the formulation of a small linear program. The low-level step leverages a geometric tracking controller, which is based on the full quadrotor model. The method is designed for the tracking of references subject to lateral constraints along the path. An example is the tracking of references along obstacle contours. It is differentiated between two different setups. Either the high-level planning step is conducted once and offline, or, alternatively, the high-level planning step is conducted recedingly online in closed-loop over a limited spatial prediction horizon.

Gust disturbances, dynamic vertical inflow and ground effect are key adverse aerodynamic phenomena that induce variations in the forces acting on a multirotor and complicate its flight control. Miniature rotorcraft typically rely on simplified modelling of such effects to compute adjustments in thrust to counteract these forces. In the most basic case, disturbance force estimations are derived from the aircraft's motion and the generated thrust is assumed to exactly match that requested by the controller. However, such systems rely on the aircraft's trajectory to be affected before disturbances can be sensed and compensated. Numerous approaches presented over the last 15-20 years aim to reject external disturbances more quickly, but challenges remain. This paper presents a new approach in this category by measuring the instantaneous force of the rotors directly at the point of generation using load-cells and implementing high-speed control to accurately track the desired thrust. Measurements from load-cells were previously considered too noisy to provide meaningful input, but the experiments presented in the paper using purpose-built hardware from low-cost commodity components in single- and dual rotor see-saw models and a flying aircraft demonstrate both the feasibility and the effectiveness of the approach in the presence of complex aerodynamic phenomena.

Deep reinforcement learning (DRL) offers powerful control for industrial cyber-physical systems (ICPSs), but its "black-box" exploration risks violating strict hardware safety limits. Typically, these constraints are managed through complex reward shaping. In this work-in-progress paper, we embed a differentiable physics model directly into the proximal policy optimization (PPO) actor loss function. By simulating short-horizon future trajectories during training, the policy is penalized for anticipated safety violations independent of the task-reward signal. Evaluated on a simulated 1-degree-of-freedom helicopter testbed with strict pitch constraints, our physics-informed soft regularizations substantially reduce constraint violations while maintaining reliable target tracking.

This paper presents a methodology for learning a control policy to intercept an intruder using the 3D direction unit vector to the intruder and the interceptor state. Prior deep reinforcement learning approaches assume either relative position or distance to the intruder is available, but this information is not readily accessible in real-world applications that employ passive, monocular camera sensors. Instead, we propose a solution that leverages an analytical policy gradient method using differentiable quadrotor dynamics to learn agile interception at speeds up to 10 m/s. The proposed approach outperforms baseline methods that utilize simplified point mass dynamics by an average of 30%.

Small multirotor aircraft are increasingly tasked with operations in the atmospheric boundary layer, where turbulent winds comparable to the vehicle's airspeed degrade trajectory tracking and can defeat conventional feedback control. This work illustrates a two-stage learning pipeline that first estimates the local wind from onboard kinematics and dynamics and then exploits that estimate inside a reinforcement learning (RL) flight controller. The wind estimator, an attention-augmented gated recurrent network trained on thousands of simulated flights through von Karman turbulence with power-law shear and veer, recovers the horizontal wind vector with a per-flight root-mean-square error of 0.40 m/s and a direction error of 3.2 degrees on unseen wind regimes, an accuracy near the floor imposed by unresolved turbulence, and generalizes to vertical ascent profiles with a skill score of 0.861 over a constant-wind reference. A proximal policy optimization controller receiving the frozen estimator's output reduces horizontal trajectory tracking error by 48% relative to a wind-blind proportional-derivative baseline across mean winds of 4 m/s to 12 m/s, winning on 100% of evaluation episodes. A three-way ablation decomposes this improvement into a kinematic component, available without wind information, and a wind-perception component; the perception share rises with wind speed, from small in light winds toward roughly half the total benefit in strong winds, consistent with the quadratic scaling of aerodynamic drag. The controller degrades gracefully on out-of-distribution winds of 13 m/s to 15 m/s, where the baseline fails catastrophically.

The control of agile quadrotors in dynamic and uncertain environments remains an open area of investigation to this day, particularly when the complete system dynamics are partially known or highly nonlinear. This work introduces a novel machine learning-based feedback-linearization control framework that employs a Gaussian Radial Basis Function (RBF) neural network (NN) to model and compensate for unmodeled dynamics in real time. The proposed controller leverages the universal approximation capability of RBF networks to model nonlinearities and uncertainties. An online adaptation of the RBF NN updates the network's weights without prior training. The control law is derived using the Lyapunov stability theory, herein guaranteeing closed-loop stability and providing theoretical guarantee of asymptotic convergence of a trajectory tracking task. Gazebo simulation and real flight experiments are conducted using the Bitcraze's Crazyflie 2.1 quadrotor subject to unmodeled air drag, actuator dynamics, and external disturbance. Despite incomplete knowledge of prior dynamics and presence of external disturbance such as air drag and drift in state estimation, the proposed controller improves trajectory tracking with rapid convergence and reduction of position-norm and yaw orientation RMSE by more than $7.13\%$ and $49.27\%$ respectively compared to baseline feedback linearization controller.

Use of quadrotor UAVs for wind velocity estimation is gaining popularity in recent studies, leveraging their maneuverability, compact size and low cost. Among available approaches, model-based wind velocity estimation is most commonly used, since it relies only on onboard sensors. However, as the quadrotor is a highly nonlinear system, thus making this task challenging. This study evaluate the use of both discrete and continuous dynamic equations of the quadrotor UAV for wind velocity estimation on SE(3), rather than commonly adapted continuous or discretized form. Lie Group Variational Integrator, developed on discrete Lagrangian is used as the discrete model without any approximation or discritization. The study assess both the discrete and continuous form of the quadrotor dynamics on SE(3) using Extended Kalman filter (EKF), and Unscented Kalman filter (UKF). The quadrotor UAV performance is evaluated in both MATLAB-based numerical simulations and free outdoor flight. The numerical simulations are conducted during both hovering and trajectory-tracking flights. Results demonstrate that, by using discrete SE(3) dynamics coupled with UKF, the quadrotor achieves higher estimation accuracy while maintaining trajectory tracking, even with low-cost sensors. These findings highlight the potential of discrete quadrotor models with UKF not only for wind velocity estimation but also for other high-accuracy tasks, even when relying on low-cost onboard sensors.

Quadrotors offer the agility needed to rapidly transport suspended payloads during time-critical applications, including search-and-rescue and medical delivery. While suspended-payload transport and traversal for these missions are well studied, the highly dynamic targeted release of the payload remains comparatively underexplored. State-of-the-art approaches typically rely on model-based trajectory optimization and tracking; however, these methods often yield sub-optimal performance due to conservative feasibility constraints, tracking errors, and the inherent difficulty of analytically modeling flexible rope dynamics. To overcome these limitations, we propose a hybrid simulation framework that couples a high-fidelity analytical quadrotor model with a physics solver for complex rope and payload interactions. By exchanging forces between the two domains at every step, we obtain a physically accurate simulation of the suspended-payload system. Leveraging this environment, we train a deep reinforcement learning (RL) policy that executes agile, accurate payload throws to designated targets. Deployed zero-shot on hardware, our RL policy pushes the boundary of the agility-accuracy trade-off, outperforming the model-based baseline by reducing the landing error by up to 50% and the throw duration by up to 30%. Ablation studies confirm that the coupled simulation is the key enabler of these gains. We further show that the same pipeline trains a policy driven by visual observations rather than an explicit state estimate, achieving accuracy comparable to that of the state-based policy. To accelerate future research in dynamic aerial manipulation, we open-source the simulator to the community upon acceptance.

Many robotics problems, including trajectory optimization, inverse kinematics, and contact-rich motion planning, reduce to nonlinear programs (NLPs). Mature NLP solvers such as IPOPT can solve these problems, offering hard constraint satisfaction, optimality guarantees, and favorable scaling with problem dimension. These solvers underpin gradient-based methods in robotics, yet remain CPU-bound and solve only one problem at a time, preventing their integration into GPU-batched learning pipelines. On the other hand, sampling-based approaches such as reinforcement learning, model predictive path integral, and imitation learning have become the core of modern robotics research due to their ability to leverage GPU-batched simulators. These simulators can generate orders of magnitude more dynamics rollouts per second than was previously possible. If a GPU-batched NLP solver existed, it would unlock similar speedups in the number of constrained, locally optimal solutions generated per second. This regime of solving many problems concurrently versus solving a single problem at a time is a key requirement for integrating NLP solvers in modern GPU-batched robotics frameworks. To this end, we introduce \texttt{jaxipm}, the first GPU-batched NLP solver, based on IPOPT, and implemented in JAX. We accomplish this by redesigning IPOPT's algorithm to eliminate control flow with \textit{heterogeneous iteration fusion}, and by minimizing GPU idle time with \textit{iteration level batching}. We evaluate \texttt{jaxipm} on a variety of quadrotor nonlinear model predictive control benchmarks, including reference tracking in the presence of obstacles, multi-quadrotor navigation without collision, and navigation in a cluttered environment. We demonstrate up to a $32.85\times$ increase in throughput over IPOPT. Our complete open-source codebase is available at https://github.com/johnviljoen/jaxipm.

Accurate dynamics models are critical for informed decision-making in robotic systems, particularly for agile aerial vehicles operating under uncertainty. Neural network dynamics models are attractive for capturing complex nonlinear effects, but existing predictive approaches struggle with long-horizon forecasting because their autoregressive rollout mechanism amplifies errors over time. Joint Embedding Predictive Architectures (JEPAs) offer a compelling alternative by modeling dynamics in latent space, yet prior JEPA-style methods for robot navigation have been studied primarily for kinematic-level planning, with limited investigation in high-frequency control. In this work, we introduce the JEPA-style model for real-time quadrotor control. The proposed approach combines a latent dynamics model with a novel physics-inspired prober that maps frozen latents to interpretable state, enabling physically grounded long-horizon prediction. Additionally, we combine the learned model with a sampling-based optimal control solution to take advantage of its predictive capabilities for real-time control on embedded hardware. Finally, to reduce the dependence on expensive and unsafe real-world data collection, we develop a structured pipeline for automated dataset generation. Extensive open-loop and outdoor closed-loop experiments demonstrate accurate prediction, robust zero-shot sim-to-real transfer, and strong generalization across diverse operating conditions.

Actor-Critic Model Predictive Control (MPC) effectively addresses complex, non-convex control problems, but guaranteeing the closed-loop stability of sequence-based learning models within these pipelines remains challenging. This paper introduces a novel Transformer-Actor-Critic MPC architecture with formal robustness guarantees. First, we prove that Transformer networks can satisfy global incremental Input-to-State Stability ($δ$ISS). We then leverage Riemannian contraction theory to analyze the interconnected dynamics between the physical plant and the predictive neural network. Finally, we integrate these theoretical bounds as a training regularizer to yield a certifiably robust policy. The framework is validated on a nonlinear 3D drone model executing target-reaching and obstacle-avoidance maneuvers.

Autonomous fall recovery is a critical capability for quadrotors operating in real-world environments, where collisions or failures may leave the vehicle resting on the ground in an arbitrary attitude. This problem is challenging because recovery must be achieved under limited onboard sensing, in constrained free space, with ground contact, and in the presence of unknown disturbances. In this letter, we present an RL-based framework for autonomous fall recovery of a quadrotor from arbitrary ground attitudes to stable hover using only lightweight onboard sensors. To address severe partial observability and intermittent sensor invalidity, we train a recurrent policy within an asymmetric actor--critic architecture, leveraging an Incremental Nonlinear Dynamic Inversion (INDI) controller to track the policy output. Combined with high-fidelity simulations of motor response and optical flow, the overall training framework significantly reduces the sim-to-real gap. Simulation ablation studies validate the importance of the main design choices, while real-world experiments demonstrate zero-shot transfer and robust recovery under different initial attitudes, wind disturbances, and additional payloads. These results demonstrate that agile quadrotor fall recovery can be achieved without explicit state estimation using only limited and unreliable onboard sensing.

We present an algorithm for efficient domain-adaptive policy learning via kernel representations. Learning domain-adaptive policies is challenging since it requires an environment representation that is both sufficiently expressive to model complex sim-to-real gaps during offline training, and computationally efficient enough to support rapid online adaptation during deployment. For instance, a quadrotor may encounter time-varying, non-stationary disturbances, such as sudden gusts of wind, payload shifts, or transitions between distinct flight regimes with and without ground effects. To address these challenges, we model unknown disturbances using a differentiable kernel approximation based on random Fourier features. During the offline training phase, we randomly sample kernel coefficients and bandwidth parameters to generate a rich diversity of disturbance profiles. We then optimize the control policy via differentiable simulation with analytical gradients, a process that takes only 50 seconds of training time on an RTX 4090 GPU. During hardware deployment, the policy adapts to non-stationary environments in real time by updating both the kernel coefficients and bandwidth through online least-squares estimation. We evaluate our method on quadrotor trajectory tracking tasks across high-fidelity numerical simulations and hardware experiments using Crazyflie, subjected to various disturbances, including complex aerodynamic effects, wind, ground effects, and payload fluctuations.

We present a generalist position control policy capable of controlling arbitrary multirotor configurations of a certain rotor count (e.g., hexarotors or quadrotors) with a single set of network weights. The policy is conditioned on a physics-grounded embodiment descriptor: a mass and inertia-normalized control allocation matrix that captures how mass-normalized motor thrusts generate linear and angular accelerations in the body-frame. To train the policy, we sample from a broad distribution of arbitrary multirotor configurations, including non-planar and asymmetric systems, and optimize a single, compact network using Proximal Policy Optimization. Training requires only five minutes on an RTX 3090 GPU using a custom NVIDIA Warp-based dynamics simulator. Through extensive simulation experiments, we show that embodiment conditioning enables robust generalist control across arbitrary morphologies. We demonstrate zero-shot real-world transfer of this generalist policy on three diverse hexarotor systems, including a planar robot, a partially symmetric non-planar system, and a random asymmetric, non-planar configuration.

Autonomous visual interception of agile aerial targets is challenging due to unpredictable target motion, limited sensing, and the strong coupling between target visibility and interceptor maneuverability. Most existing strapdown-camera interception methods preserve visibility using conic line-of-sight (LOS) constraints that keep the target near the image center. While safe, such symmetric constraints unnecessarily restrict maneuverability and can significantly reduce the usable thrust for pursuit. Motivated by the observation that aggressive FPV pilots do not maintain equal visibility margins in all image directions, this paper proposes a Planar-Sector Line-of-Sight (PS-LOS) guidance framework for autonomous interception using a lifting-wing quadcopter equipped with only a strapdown monocular camera. PS-LOS tightly constrains lateral image error while relaxing longitudinal image error within a safe field-of-view margin, preserving visibility while releasing maneuverability for acceleration-intensive pursuit. Under the lifting-wing quadcopter model, PS-LOS provides nearly 50% more available thrust near the LOS direction than conventional conic LOS constraints. To realize LOS-only interception without direct depth measurements, a delay-compensated state-estimation framework and a nonlinear guidance-and-control architecture are developed for lifting-wing quadcopters. Extensive outdoor flight experiments demonstrate autonomous interception of agile targets exhibiting large-amplitude, high-frequency, and unpredictable motion under real wind disturbances. The proposed system achieves successful interceptions at ranges up to 138 m while maintaining continuous visual tracking throughout the engagement. The results validate PS-LOS as a visibility-preserving, maneuverability-aware guidance framework for long-range visual interception of agile aerial targets.

Multirotors are widely used in applications ranging from surveillance to precision agriculture, yet conventional designs remain limited by their under-actuation. Tilt-rotor configurations overcome this limitation by enabling full actuation. This paper investigates neural-network-based control strategies for a fully actuated tilt-rotor system with four thrust-vectoring inputs. Our work is structured in two parts. First, we deliberately present a negative result by evaluating a direct input-output control approach. In this method, multilayer perceptrons (MLPs), long short-term memory (LSTM) networks, and transformer models are trained to map system states and their desired values directly to control signals. We show that this strategy fails to stabilize the system, highlighting the inherent difficulty of applying direct input-output learning to highly unstable plants. Second, as the main contribution, we propose a neural-network-enhanced sliding mode controller (SMC). The method decomposes the system dynamics into input-independent and input-dependent components, with the former learned from a small dataset using lightweight networks, thereby reducing real-time computational demands. Moreover, the proposed method can be trained using flight logs collected from low-performance controllers, and the resulting dynamic model learned from real-world data can be used in simulation. We further compare MLP- and LSTM-based implementations under model uncertainties and external disturbances, demonstrating the robustness and effectiveness of the proposed approach; in particular, the controller with the LSTM plant dynamics predictor achieves superior performance to its MLP-based counterpart while also exhibiting lower runtime.

This paper proposes a Network Distributed Multi-Agent Reinforcement Learning (ND-MARL) framework for quadcopter consensus control. Compared to conventional multi-agent MARL formulations that rely on centralized planning or fully decentralized execution, ND-MARL incorporates the swarm communication graph into the decision process. Under a 2-Neighbor communication topology, each agent observes information of only two neighbors and outputs an action through a distributed policy. A high-level distributed consensus planner is trained using Multi-Agent Soft Actor-Critic (MASAC) and embedded in a hierarchical stack to generate reference target positions tracked by a low-level quadcopter controller. Results demonstrate smooth consensus trajectories and planner-tracker integration when compared to a centralized MARL controller. Most notably, the learned controller exhibits zero-shot scalability, as policies trained on a three-agent system are deployed to swarms of up to 250 agents under the same 2-Neighbor communication topology without retraining or fine-tuning, achieving consistent convergence with increasing steady-state spread at large team sizes due to sparse information propagation. These findings highlight ND-MARL as a stable framework for distributed, communication-aware quadcopter consensus control.

A fixed-wing UAV must hold airspeed, altitude, and heading references under wind, gusts, and turbulence, channels coupled so that correcting one can degrade another. Classical autopilots stabilize the airframe well but adapt poorly when a hard crosswind meets an aggressive turn, while reinforcement-learning (RL) policies acting directly on the surfaces concentrate exploration risk at the actuator interface. We place a learned supervisor above an unchanged autopilot rather than inside it: it selects a residual from a finite, bounded action set on the commanded airspeed, altitude, and heading; the modified reference is projected into an admissible command envelope before reaching the autopilot, which stays the only actuator-facing controller. What is new is how the residual is chosen. HJB residual scores candidates with a semi-discrete value-iteration critic in the spirit of the Hamilton-Jacobi-Bellman (HJB) equation, ranks them by a no-op-relative Hamiltonian advantage, and filters them through a control-Lyapunov- and control-barrier-inspired finite-action shield that always keeps a no-op fallback. On a shared 12-state runtime holding the plant, autopilot, and actuator model fixed, so the comparison is at the package level, HJB residual lowers mean RMS path-tracking error to 44.809 m, against 338.617 m for the baseline autopilot and 88.809 m for a tabular-Q residual, an 86.77% reduction over the baseline and 49.54% over Q-learning. The gain concentrates where the baseline fails worst and comes with a measured rise in airspeed error, so no method dominates every metric. We present this autopilot-preserving residual command-supervision design and benchmark with its trade-offs reported intact.

This paper addresses the problem of using a deep Reinforcement Learning (RL)-based low-level Quadrotor controller within an autonomous Quadrotor navigation stack for aerial inspection missions in under-canopy forest environments. Specifically, the article presents an end-to-end (mapping states to RPMs) Quadrotor control policy that achieves inspection view-pose tracking (simultaneous position and yaw reference tracking), which is crucial for various target inspection behaviors and point-to-point navigation in forests. To ensure safe and reliable deployment of the end-to-end RL controller in long-range missions, this article utilizes a higher navigation guidance layer comprising of a Traveling Salesman Problem planner (TSP) and a Rapidly-exploring Random Tree Star (RRT*) planner. Over a known map of a forest and a set of user-specified inspection regions, the TSP planner finds the optimal visitation sequence. Between two target regions, collision-free paths that respect the tracking limitations of the lower end-to-end RL policy are generated by an RRT* planner. Through five target inspection scenarios, this article demonstrates that an RL-based motor-level stabilizing controller, supported by a navigation guidance layer, can be used effectively as the low-level inspection execution module for under-canopy forest inspection missions.

Reinforcement learning (RL)-based quadrotor control policies have achieved impressive performance in tasks such as fast navigation in cluttered environments and drone racing, where the focus is on speed and agility. However, in several applications, such as infrastructure inspection, it is critical to achieve precise, controlled maneuvers with tunable performance. In this article, we present a novel heuristic approach to achieve tunable performance in RL-based Quadrotor control through reward design and termination conditions. We present a novel reward structure containing dual bandwidth exponentials that achieves a baseline critically damped response in setpoint tracking, with low steady-state errors. When trained with a Proximal Policy Optimization (PPO) algorithm, in conjunction with episode truncation conditions, the desired performance is achieved in 6 million time steps in a sample-efficient manner. In order to tune the performance about the baseline behavior, we present intuitive heuristic rules to adjust the reward weights and exponential coefficients to achieve faster (acrobatic-like) and slower (inspection-like) settling time performance, while retaining the baseline critically damped response and approximately 2% steady-state error. We evaluate the three RL policies (baseline, acrobatic, and inspection) across 100 trials and show accurate and tunable performance in position and yaw tracking from random initial conditions, thereby demonstrating the effectiveness of the proposed heuristic approach.

Deep Reinforcement Learning (DRL) for quadrotor flight control typically relies on Domain Randomization (DR) for sim-to-real transfer, resulting in overly conservative policies that struggle with dynamic disturbances. To overcome this, we propose a novel adaptive control architecture that actively perceives and reacts to instantaneous perturbations. First, we train an optimal outer-loop policy, then replace its reliance on ground-truth disturbance data with a Residual Dynamics Predictor (RDP). The RDP estimates the external forces and moments acting on the aircraft in flight online using only the history of states and control actions. For seamless hardware transfer, we introduce a data-efficient linear calibration bridge and an online thrust correction mechanism that align the simulated latent space with reality using mere seconds of flight data. Real-world validations on a Crazyflie micro-quadrotor demonstrate that our adaptive controller significantly outperforms baselines, maintaining precise trajectory tracking under severe uncertainties including mass variations, asymmetric payloads, and dynamic slung loads

This paper presents a prototyping framework for distributed control of multi-robot systems, aimed at bridging theory and practical testing of distributed optimization algorithms. Using the Single Program, Multiple Data (SPMD) paradigm, the framework emulates distributed control on a single computer, with each core running the same algorithm using local states and neighbour-to-neighbour communication. We demonstrate the framework on a four-quadrotor position-swapping task using a non-cooperative game-theoretic distributed algorithm. Computational time and trajectory data are compared across the supported dynamics levels: a point-mass model, a high-fidelity quadrotor model, and an experimental hardware testbed using Crazyflie quadcopters. The results show that the framework provides a low-cost and accessible approach for validating distributed algorithms.

Fully actuated multirotor platforms decouple translational force generation from vehicle attitude, enabling independent control of position and orientation and shifting performance limitations from attitude authority to actuator dynamics and control effectiveness. This paper compares a model-based nonlinear dynamic inversion controller (geometric NDI) with a sensor-based incremental dynamic inversion controller (INDI) on a fixed-tilt fully actuated hexarotor. Both controllers share an identical outer-loop structure and are both executed at 500 Hz; therefore, performance differences can be attributed primarily to the inversion strategy. Controller performance is evaluated in five experiments covering attitude step tracking under nominal conditions and under a 50% mismatch in the rotor force coefficient, hover disturbance rejection under an external lateral load, waypoint tracking in the presence of wind gust disturbances, reduced control frequency, and injected sensor degradation. The results show that INDI offers clear advantages under parameter mismatch, gust disturbances, and sensor degradation, and maintains lower position errors across the controller-frequency sweep. However, its advantages are not universal: geometric NDI yields better attitude tracking at reduced control frequencies. To the authors' best knowledge, this work presents the first experimental validation of a full pose tracking INDI controller with decoupled translational and rotational dynamics. These findings highlight the trade-off between measurement-based and model-based inversion for robust control and rapid deployment of fully actuated UAVs.

The goal of this paper is certifying safety of dynamical systems subject to uncertainty. Existing approaches use trajectory data to estimate transition probabilities, and compute safety probabilities recursively via dynamic programming (DP). This recursion may lead to compounding errors in the certified safety probability, thus collapsing to a vacuous lower bound for growing horizons $T$. We propose a kernel embedding framework that treats safety certification as a classification problem on trajectory data, directly estimating the $T$-step safety probability without recursion. We show that the framework subsumes well-established approaches from the literature (e.g., barrier certificates, robust Markov models) as special cases, and allows us to go beyond their limitations. As the main consequence, it bypasses compounding error across the horizon and enables certification for systems with non-Markovian dynamics. We demonstrate that direct estimators remain stable independent of the certification horizon and in the non-Markovian setting, whilst DP-based certificates silently go unsound -- confirmed in simulation on a neural-controlled quadrotor.

It has recently been shown that all physical parameters of an Incremental Nonlinear Dynamic Inversion (INDI) controller can be estimated onboard a multirotor within half a second, which is fast enough to do the full identification during a throw in the air. However, a robust method to tune outer loop gains for this feedback-linearizing INDI controller depending on the model parameters is still missing. This work presents the design of a robust gain-scheduled controller for attitude control of quadrotor, using an INDI-based inner loop with online identification of its system parameters. A gain-scheduled cascaded attitude controller with a feedforward filter is synthesized for a symmetric quadrotor using signal-based $\mathcal{H}_\infty$ closed-loop shaping. The resulting controller exhibits good stability margins, with nonlinear simulations confirming effective tracking performance under uncertainty. Experimental evaluation is also conducted through flight tests with full online parameter identification. Even though the identified parameters during these tests are far outside the defined uncertainty range, acceptable flight performance comparable to simulation results is maintained for actuator time constants below 40 ms.

Imitation learning is a well-established approach for machine-learning-based control. However, its applicability depends on having access to demonstrations, which are often expensive to collect and/or suboptimal for solving the task. In this work, we present GCImOpt, an approach to learn efficient goal-conditioned policies by training on datasets generated by trajectory optimization. Our approach for dataset generation is computationally efficient, can generate thousands of optimal trajectories in minutes on a laptop computer, and produces high-quality demonstrations. Further, by means of a data augmentation scheme that treats intermediate states as goals, we are able to increase the training dataset size by an order of magnitude. Using our generated datasets, we train goal-conditioned neural network policies that can control the system towards arbitrary goals. To demonstrate the generality of our approach, we generate datasets and then train policies for various control tasks, namely cart-pole stabilization, planar and three-dimensional quadcopter stabilization, and point reaching using a 6-DoF robot arm. We show that our trained policies can achieve high success rates and near-optimal control profiles, all while being small (less than 80,000 neural network parameters) and fast enough (up to more than 6,000 times faster than a trajectory optimization solver) that they could be deployed onboard resource-constrained controllers. We provide videos, code, datasets and pre-trained policies under a free software license; see our project website https://jongoiko.github.io/gcimopt/.

Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process regression are established techniques, thanks to their inherent uncertainty quantification mechanism. Still, existing bounds either pose strong assumptions on the underlying noise distribution, are conservative, do not directly apply in the multi-output case, or are difficult to integrate into downstream tasks. This paper addresses these limitations by presenting a tight, deterministic bound for multi-output functions in Reproducing Kernel Hilbert Spaces (RKHSs) subject to bounded noise. It is obtained through an unconstrained, duality-based formulation, which shares the same structure as classic Gaussian process confidence bounds, and can thus be straightforwardly integrated into downstream optimization pipelines. We show that the proposed bound generalizes existing results and illustrate its application using an example inspired by quadrotor dynamics learning.

Existing aerial-robotics benchmarks target vehicles from hundreds of grams to several kilograms and typically expose only high-level state data. They omit the actuator-level signals required to study nano-scale quadrotors, where low-Reynoldsnumber aerodynamics, coreless DC motor nonlinearities, and severe computational constraints invalidate models and controllers developed for larger vehicles. We introduce NanoBench, an open-source multi-task benchmark collected on the commercially available Crazyflie 2.1 nano-quadrotor (takeoff weight 27 g) in a Vicon motion capture arena. The dataset comprises 172 flight recordings spanning multi-frequency excitation, geometric trajectory tracking at three speed regimes, and long-duration battery-drain hover. Each recording provides synchronized Vicon ground truth, raw IMU data, onboard extended Kalman filter (EKF) estimates, PID controller internals, and motor PWM commands at 100 Hz, alongside battery telemetry at 10 Hz, crossaligned by gyroscope-based correlation on a 1 ms search grid. NanoBench defines standardized evaluation protocols, train/test splits, and open-source baselines for three tasks: nonlinear system identification, closed-loop controller benchmarking, and onboard state estimation assessment. To our knowledge, it is the first public dataset to jointly provide actuator commands, controller internals, and estimator outputs with millimeter-accurate ground truth on a commercially available nano-scale aerial platform.

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 directly control the system, 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 being 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 simulations and real flights, under equal computational budgets, UNIQUE improves closed-loop tracking by up to 75% compared with standard MPC and hierarchical baselines. Ablations and Pareto analyses confirm performance gains across variations in horizon, constraint approximations, and smoothing schedules.

This paper presents a systematic framework for computing formally guaranteed trajectory tracking error bounds for autonomous helicopters based on Robust Positive Invariant (RPI) sets. The approach establishes a closed-loop translational error dynamics which is cast into polytopic linear parameter-varying form with bounded additive and state-dependent disturbances. Ellipsoidal RPI sets are computed, yielding explicit position error bounds suitable as certified buffer zones in upper-level trajectory planning. Three controller architectures are compared with respect to the conservatism of their error bounds and tracking performance. Simulation results on a nonlinear helicopter model demonstrate that all architectures satisfy the derived bounds, while highlighting trade-offs between performance and the conservatism of the computed invariant set.