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A Review of Control Algorithms for Autonomous Quadrotors
Andrew Zulu, Samuel John
TL;DR
Quadrotor control is difficult because the vehicle is nonlinear, under-actuated, coupled, and subject to uncertainties. The paper reviews multiple control algorithms and their trade-offs, concluding that hybrid schemes may combine useful properties, although application-specific compromises remain necessary.
Problem
Quadrotor control is challenging because coupled, under-actuated, nonlinear dynamics and mission uncertainties complicate flight control.
Method
The paper briefly describes the quadrotor system and reviews prominent linear and nonlinear control algorithms, including their advantages and disadvantages.
Results
The review finds that no single algorithm provides all required features, while hybrid schemes can combine robustness, adaptability, optimality, simplicity, tracking, response, and disturbance rejection.
Takeaways & Limitations
Hybrid control schemes should be considered, but each application requires a compromise over which performance factors are most appropriate.
Takeaways & Limitations
PID tuning must be conducted around the hover equilibrium point to obtain good performance.
Abstract
from arXiv · showhide
The quadrotor unmanned aerial vehicle is a great platform for control systems research as its nonlinear nature and under-actuated configuration make it ideal to synthesize and analyze control algorithms. After a brief explanation of the system, several algorithms have been analyzed including their advantages and disadvantages: PID, Linear Quadratic Regulator (LQR), Sliding mode, Backstepping, Feedback linearization, Adaptive, Robust, Optimal, L1, H-infinity, Fuzzy logic and Artificial neutral networks. The conclusion of this work is a proposal of hybrid systems to be considered as they combine advantages from more than one control philosophy.
1. Introduction
The paper reviews quadrotor control in response to the vehicle’s coupled, under-actuated, nonlinear, and uncertain dynamics. It focuses on identifying suitable configurations and control schemes for quadrotor MAV applications.
- Their simple design, agility, maneuverability, payload, and VTOL capability motivate applications such as wildlife counting in protected African game reserves.
- Counting wildlife from roads misses animals away from roads, while hovering helicopters can cause animals to flee and produce inaccurate counts.
- Quadrotors use fixed-pitch rotors and motor-speed variation for vehicle control, avoiding complex mechanical control linkages.
- Quadrotor control is challenging because the vehicle has coupled dynamics, an under-actuated configuration, nonlinear dynamics, and mission-related uncertainties.
- The paper reviews prominent quadrotor controllers after introducing the mathematical model, then discusses hybrid systems and presents a tabular comparison.
2. Mathematical Model
The mathematical model describes how rotor-speed changes generate lift and control quadrotor motion. It introduces the coordinate system, rotor actions, Newton–Euler equations, and parameters governing inertial, thrust, and drag effects.
- The quadrotor generates lift by controlling the speeds of fixed-pitch rotors.
- Equal rotor speeds produce hover when total thrust equals system weight, while differential thrust controls roll, pitch, and yaw.
- Roll uses differential thrust from rotors 2 and 4, whereas pitch uses differential thrust from rotors 1 and 3.
- Yaw uses differential thrust from opposite rotor pairs while the remaining pair is adjusted to maintain altitude.
- The equations of motion are introduced using Newton–Euler formalism, with rotor inputs expressed through thrust and drag coefficients.
3. Survey of Control Algorithms
The review compares linear and nonlinear quadrotor controllers, emphasizing their design benefits alongside limitations arising from nonlinear and imperfectly modeled dynamics. PID examples show both effective stabilization and tracking limitations.
- Quadrotor controllers are broadly categorized as linear or nonlinear, with each control scheme having advantages and disadvantages.
- Proportional Integral Derivative (PID): PID control is simple to design, easy to tune, and robust, but nonlinear and inaccurately modeled dynamics limit its performance on quadrotors.
- Proportional Integral Derivative (PID): PID attitude control combined with dynamic surface altitude control yielded uniformly ultimately bounded signals and stable hovering.
- Proportional Integral Derivative (PID): PID performed better in pitch tracking, while roll tracking exhibited large steady-state errors.
- Proportional Integral Derivative (PID): A separate PID study reported good attitude stabilization, good response time, almost zero steady-state error, and slight overshoot.
- Proportional Integral Derivative (PID): PID tuning can be challenging because it must be conducted around the hover equilibrium point to obtain good performance.
3.2. Linear Quadratic Regulator/Gaussian-LQR/G
LQR minimizes a suitable cost function, while LQG extends it with estimation for Gaussian noise and incomplete state information. The supplied studies report accurate path following and good hover stabilization, alongside robustness and tracking findings for sliding-mode control.
- LQR: LQR minimizes a suitable cost function and was reported to outperform PID when applied to a more complete quadrotor dynamic model.Both approaches provided average results, but the comparison implicitly favored LQR because the PID used simplified dynamics while LQR used the complete model.
- LQR: Accurate path following was achieved in simulation with optimal real-time trajectories despite wind and other disturbances, although tracking was lost after obstacle avoidance.Performance with many obstacles remained unanalyzed.
- LQG: LQG combines LQR with a Linear Quadratic Estimator and Kalman Filter for Gaussian noise and incomplete state information.Integral-action LQG also produced good hover stabilization without requiring complete state information.
- Sliding Mode Control: Sliding-mode control uses a discontinuous signal to drive the system along a prescribed path without linearizing its dynamics.The supplied studies report good stability, robustness, and tracking, while chattering was minimized using a continuous approximation of a sign function.
3.4. (Integrator) Backstepping Control
Backstepping recursively decomposes the quadrotor controller into steps that progressively stabilize subsystems. Studies report good tracking and stability, while integrator backstepping is introduced to improve robustness and transient behavior.
- Backstepping: Backstepping recursively breaks the controller into steps and progressively stabilizes each quadrotor subsystem.The approach is described as fast-converging, computationally economical, and able to handle disturbances, but with limited robustness.
- Backstepping: Good position and yaw tracking was achieved, while Lyapunov analysis stabilized the roll and pitch angles.The reported system included under-actuated, fully actuated, and propeller subsystems.
- Backstepping: Lyapunov analysis found the closed-loop attitude system asymptotically stable with all states uniformly ultimately bounded under external disturbance.Quaternion formulation also supported computational stabilization and avoided singularity.
- Integrator Backstepping: Adding an integrator produces integrator backstepping, which was shown to eliminate steady-state errors, reduce response time, and restrain overshoot.The modification is presented as a way to increase robustness to external disturbances.
3.5. Adaptive Control Algorithms
Adaptive controllers address uncertain or time-varying system parameters, with reported stabilization under changing mass properties, inertia, damping, and center of gravity. The supplied discussion also contrasts robustness-oriented control with tracking performance.
- Adaptive Control: Adaptive control algorithms adapt to system parameters that are uncertain or vary with time.One continuous time-varying controller was reported to perform well with known uncertainties in mass, moments of inertia, and aerodynamic damping coefficients.
- Adaptive Control: With a dynamically changing center of gravity, adaptive feedback linearization stabilized the quadrotor when PD and regular feedback linearization could not.The work concerns a quadrotor that could self-configure in real time as its center of gravity changes.
- Adaptive Control: An adaptive technique based on the L1 norm traded control performance against robustness, while its modified linearized model compensated for constant and moderate wind gusts.The passage explicitly describes a performance–robustness tradeoff.
- Robust Control: Robust control is designed for parameter uncertainty and disturbances, but poor tracking ability is identified as a common limitation.A robust tracking algorithm nevertheless achieved asymptotic stability under parametric uncertainties and unknown nonlinear disturbances without observers or online adaptive updating laws.
3.7. Optimal Control Algorithms
The review describes optimization and feedback-linearization approaches for quadrotor control, highlighting trade-offs among cost minimization, disturbance rejection, robustness, tracking, and computational efficiency.
- Optimization algorithms: Optimization algorithms minimize a variable through a cost function, with LQR, L1, H∞, and Kalman filtering identified as common examples.The review notes that optimization algorithms generally have poor robustness, although a relatively robust and L1-optimal controller efficiently minimized errors and rejected persistent disturbances.
- Optimization algorithms: H∞ looping achieved superior disturbance rejection under saturation, but its Riccati-equation antI-windup compensator lacked apparent computational efficiency.The method was applied to simplified quadrotor dynamics for iterative parameter identification and attitude control.
- Optimization algorithms: An integral optimal predictive H∞ controller provided sustained disturbance rejection and good robustness for rotational stabilization and model-predictive path following.Integral action was identified as key to achieving good tracking.
- Feedback linearization: Feedback linearization transforms a nonlinear model into an equivalent linear system through a change of variables, but requires an exact model and can lose precision.An adaptive output-feedback implementation stabilized and reconfigured a quadrotor when its center of gravity changed.
- Feedback linearization: Feedback linearization and input dynamic inversion produced convergence of velocity and yaw angle in two simulated path-following cases.The controller allowed designers to specify speed profile and yaw angle as functions of displacement along the path.
- Feedback linearization: Feedback linearization showed good tracking but poor disturbance rejection, while combining it with a less noise-sensitive algorithm improved performance.Compared with adaptive sliding mode control, feedback linearization was sensitive to sensor noise and not robust.
3.9. Intelligent Control (Fuzzy Logic and Artificial Neural Networks)
The review presents fuzzy logic and neural networks as intelligent control approaches for quadrotors, while noting their uncertainty, mathematical complexity, tuning challenges, and computational demands.
- Intelligent control: Intelligent control includes fuzzy logic, neural networks, machine learning, and genetic algorithms, but its complexity and computational-resource requirements limit use.Fuzzy logic and neural networks are described as the most widely used intelligent-control approaches.
- Fuzzy logic: A fuzzy controller achieved good simulated position and orientation response, but its input tuning relied on trial and error.The trial-and-error tuning approach was identified as a major limitation.
- Artificial neural networks: A robust neural-network algorithm improved desired-attitude achievement and reduced weight drift under modeling error and considerable wind disturbance.The method was applied to quadrotor stabilization.
- Artificial neural networks: A neural-network output-feedback controller learned modeled and unmodeled UAV dynamics for leader-follower formation control.A virtual neural network controlled six degrees of freedom from four control inputs, with Lyapunov analysis covering tracking and estimation errors.
- Artificial neural networks: An adaptive neural-network scheme reduced tracking error and avoided weight drift during quadrotor stabilization with sinusoidal disturbance.The solution used two parallel single-hidden-layer networks.
- Fuzzy logic: Figure 6 depicts the general block diagram of a fuzzy logic controller implemented on the quadrotor.The caption identifies the diagram as an FLC controller applied to the quadrotor.
3.10. Hybrid Control Algorithms
The review motivates hybrid quadrotor controllers because individual linear and nonlinear algorithms have limitations, then presents combinations designed to reduce chattering, reject disturbances, improve robustness, and handle unmodeled dynamics.
- Motivation: No single controller provides all desired properties, so researchers combine philosophies from multiple control algorithms.The review explicitly presents its hybrid examples as non-exhaustive.
- Hybrid combinations: A hybrid fuzzy, backstepping, and sliding-mode controller successfully eliminated sliding-mode chattering.The combination targets a known limitation of sliding-mode control.
- Fuzzy logic implementation: Figure 6 shows a block diagram of a fuzzy logic controller applied to the quadrotor.The figure is identified as an FLC controller diagram, while the accompanying text calls it a general implementation block diagram.
- Hybrid combinations: A feedback-linearization controller operated in parallel with a high-order sliding-mode controller used as an observer and estimator of external disturbances.The system showed good disturbance rejection and robustness.
- Hybrid combinations: Adaptive backstepping combined with neural networks achieved translational-position and yaw tracking while maintaining roll-pitch stability and compensating for unmodeled dynamics.The controller did not require the dynamic model or other parameters, increasing reported versatility and robustness.
4. Comparison of Control Algorithms
The review’s comparison table is intended as a broad, qualified guide to the relative performance of quadrotor control algorithms under otherwise equal conditions.
- Comparison: Table 1 summarizes comparisons among quadrotor control algorithms, but performance depends on factors that may not be modeled.The authors therefore characterize the table as a “fuzzy” guide based on the paper and common knowledge.
5. Discussion and Conclusion
The survey finds that no single quadrotor control algorithm provides all desired features, motivating carefully selected hybrid schemes and future work on fully actuated tilting-propeller designs.
- Discussion and Conclusion: The survey serves as a stepping stone toward quadrotors with tilting propellers and six control inputs for six control outputs.Tilting propellers increase the number of actuated inputs and make the quadrotor fully actuated.
- Discussion and Conclusion: The planned follow-up work will investigate optimal control algorithms for asymptotic stability of tilting-propeller quadrotors under any conditions.The authors describe this research direction as relatively new, with few literature examples and promising performance achievements.
- Discussion and Conclusion: The authors propose hybrid control schemes because no single algorithm offers all required features.Desired properties include robustness, adaptability, optimality, simplicity, tracking ability, fast response, and disturbance rejection.
- Discussion and Conclusion: Hybrid systems still require a compromise because they do not guarantee good performance for every control application.The appropriate balance among control factors depends on the application.
- Discussion and Conclusion: For the intended game-counting application, the designed quadrotor should provide high endurance, low noise, high agility, high cruising ability, and VTOL capability.These characteristics are presented as important for supporting nature conservationists and obtaining accurate animal statistics.