E.J.J. Smeur
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In the aerospace control domain, Nonlinear Dynamic Inversion (NDI)-based control laws are widely spread. As a variation to Incremental Nonlinear Dynamic Inversion (INDI), the sensory Nonlinear Dynamic Inversion (sNDI) method was recently developed. Both methods rely on replacing model knowledge with sensor measurements. However, the methods differ in how the pseudo-controls are allocated: INDI allocates them incrementally, while sNDI allocates them globally, with corresponding advantages and disadvantages. While INDI requires a restoring mechanism in the control allocation due to path dependency issues in overactuated nonlinear systems, sNDI does not experience this problem. In addition to the comparison, the paper demonstrates that both methods lead to identical results if restoring is applied in the control allocation of INDI. Even though sNDI and INDI with restoring can lead to limit cycles for theoretical non-linear overactuated systems, the practical applicability of this approach to transition electrical vertical take-off and landing vehicles (eVTOL) is demonstrated in flight tests of the Variable Skew Quad Plane.
This work introduces a novel analytical model for estimating the airspeed of fixed-wing Unmanned Aerial Vehicles (UAVs) using solely propeller power and rotational speed measurements. The model can be used to replace Pitot-tube-based airspeed sensors, or contribute to redundancy in airspeed estimation. It does not require knowledge of the vehicle’s dynamic model and is computationally lightweight. It leverages power and rotational speed feedback, which is readily available from modern Electronic Speed Controllers (ESCs), thereby enabling seamless integration with existing systems and off-the-shelf components. A systematic approach is followed to derive the model structure based on least squares optimization and regularization techniques on Blade Element Momentum (BEM) simulation, wind tunnel, and flight test datasets. The final model generalizes well achieving a normalized Root Mean Square Error (nRMSE) of 5 % on unseen flight data. The model coefficients can be identified either offline, using flight logs with airspeed measurements, or in-flight, using a lightweight identification method based only on Global Positioning System (GPS) velocity data. The resulting system provides a robust and computationally efficient solution for real-time airspeed estimation across diverse fixed-wing UAV platforms.
Incremental Nonlinear Dynamic Inversion (INDI) has become a popular control strategy for unmanned aerial vehicles due to its disturbance rejection capabilities and minimal model reliance. However, its standard formulation neglects actuator dynamics, leading to undesired coupling in systems with heterogeneous actuator characteristics such as in the Variable Skew Quad Plane (VSQP). This paper analyzes the limitations of INDI in such scenarios and demonstrates how Actuator Nonlinear Dynamic Inversion (ANDI) solves them. The closed-loop transfer function analysis shows how ANDI eliminates cross-axis coupling by directly incorporating actuator dynamics into the control allocation process. Additionally, ANDI is compared to a modified INDI approach that employs lead-lag filters to homogenize actuator behavior. While this approach is effective in decoupling, it unnecessarily slows down system response and worsens saturation handling. Simulation and flight test results using the VSQP validate the theoretical findings, confirming that ANDI offers improved control accuracy on coupled axes without compromising performance on decoupled axes.
The inertia tensor is an important parameter in many engineering fields, but measuring it can be cumbersome and involve multiple experiments or accurate and expensive equipment. We propose a method to measure the moment of inertia tensor of a rigid body from a single spinning throw by attaching a small and inexpensive stand-alone measurement device consisting of a gyroscope, accelerometer, and a reaction wheel. The method includes a compensation for the increase of moment of inertia due to adding the measurement device to the body, and additionally obtains the location of the centre of gravity of the body as an intermediate result. Experiments performed with known rigid bodies show that the mean accuracy is around 2%. Monte Carlo simulations reveal invariance to direction of spin and positioning of the measurement device, but show some sensitivity to noise.
Tailsitter aircraft attract considerable interest due to their capabilities of both agile hover and high speed forward flight. However, traditional tailsitters that use aerodynamic control surfaces face the challenge of limited control effectiveness and associated actuator saturation during vertical flight and transitions. Conversely, tailsitters relying solely on tilting rotors have the drawback of insufficient roll control authority in forward flight. This letter proposes a tilt-rotor tailsitter aircraft with both elevons and tilting rotors as a promising solution. By implementing a cascaded weighted least squares (WLS) based incremental nonlinear dynamic inversion (INDI) controller, the drone successfully achieved autonomous waypoint tracking in outdoor experiments at a cruise airspeed of 16 m/s, including transitions between forward flight and hover without actuator saturation. Wind tunnel experiments confirm improved roll control compared to tilt-rotor-only configurations, while comparative outdoor flight tests highlight the vehicle's superior control over elevon-only designs during critical phases such as vertical descent and transitions. Finally, we also show that the tilt-rotors allow for an autonomous takeoff and landing with a unique pivoting capability that demonstrates stability and robustness under wind disturbances.
This paper presents a method to recover quadrotor Unmanned Air Vehicles (UAVs) from a throw, when no control parameters are known before the throw. We leverage the availability of high-frequency rotor speed feedback available in racing drone hardware and software to find control effectiveness values and fit a motor model using recursive least squares (RLS) estimation. Furthermore, we propose an excitation sequence that provides large actuation commands while guaranteeing to stay within gyroscope sensing limits. After 450ms of excitation, an Incremental Nonlinear Dynamic Inversion (INDI) attitude controller uses the 52 fitted parameters to arrest rotational motion and recover an upright attitude. Finally, a Nonlinear Dynamic Inversion (NDI) position controller drives the craft to a position setpoint. The proposed algorithm runs efficiently on microcontrollers found in common UAV flight controllers, and was shown to recover an agile quadrotor every time in live experiments with as low as 3.5m throw height, demonstrating robustness against initial rotations and noise. We also demonstrate control of randomized quadrotors in simulated throws, where the parameter fitting Root-Mean-Square (RMS) error is typically within 10% of the true value.
The authors regret to inform that an incorrect transfer function was included in Eq. (12). The correct transfer function is: [Formula Presented] The selected gains were [Formula Presented]. This leads to a real pole at 0.964 and two complex poles at 0.965 ± 0.0445i. The difference of the model compared to the measured step response has now reduced, the largest difference being 4.8% of the final step value at 0.14 s. The mistake does not influence any of the conclusions drawn in the paper. The authors would like to apologize for any inconvenience caused.
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This paper presents the design of an Incremental Nonlinear Dynamic Inversion (INDI) controller for the novel, patent pending (NL 2031701) platform Variable Skew Quad Plane (VSQP). Part of the identified challenges is the development of a model for the actuator effectiveness and lift especially as a function of skew, the newly added degree of freedom. The models and assumptions are verified through static and dynamic wind tunnel tests at the Open Jet Facility (OJF) of TU Delft. Transition tests have been successfully performed thanks to an automatic skew controller derived from the proposed models and aimed to maximize control authority.
Hybrid Unmanned Aerial Vehicles UAV are vehicles capable of take-off and landing vertically like helicopters while maintaining the long-range efficiency of fixed-wing aircraft. Unfortunately, due to their wing area, these vehicles are sensitive to wind gusts when hovering. One way to increase the hovering wind-rejection capabilities of hybrid UAV is through the addition of extra actuators capable of directing the thrust of the rotors. Nevertheless, the ability to control UAVs with many actuators is strictly related to how well the Control Allocation problem is solved. Generally, to reduce the problem complexity, conventional (CA) methods make use of linearized control effectiveness in order to optimize the inputs that achieve a certain control objective. We show that this simplification can lead to oscillations if it is applied to thrust vectoring vehicles, with pronounced non-linear actuator effectiveness. When large control objectives are requested or actuators saturate, the linearized effectiveness based CA methods tend to compute a solution far away from the initial actuator state, invalidating the linearization. A potential solution could be to impose limits on the solution domain of the linearized CA algorithm. However, this solution only reduces the oscillations at the expense of a lag in the vehicle acceleration response. To overcome this limitation, we present a fully nonlinear CA method, which uses an Sequential Quadratic Programming (SQP) algorithm to solve the CA problem. The method is tested and implemented on a single board computer that computes the actuator solution in real time onboard a dual axis tilting rotor quad-plane. Flight test experiments confirm the problem of severe oscillations in the linearized effectiveness CA algorithms and show how the only algorithm able to optimally solve the CA problem is the presented Nonlinear method.
Tailsitter Micro Air Vehicles with two rotors are promising due to their simplicity and efficient forward flight, but actuator saturation due to ineffective pitch control at a high angle of attack flight is a challenge limiting the flight envelope. This paper proposes a novel tilt-rotor tailsitter design which features two tilting rotors as the only means for control moment generation. Incremental Nonlinear Dynamic Inversion (INDI) is applied to the attitude control problem of the tiltrotor tailsitter, whose attitude angle tracking performance is validated by indoor and outdoor flight tests. It is found that actuator saturation is largely avoided by using thrust vectoring which provides sufficient capability of pitch moment generation. However, it is also found that the proposed design with only leading-edge tilting motors excluding any aerodynamic control surfaces has limited roll control effectiveness in forward flight.
Unmanned Aerial Vehicles (UAVs) have the potential to perform many different missions, some of which may require a large aircraft for endurance and a small aircraft for maneuverability in wind gusts or cluttered environments such as buildings. This paper proposes a novel combination of a quadrotor and a hybrid biplane capable of joint hover, joint forward flight, and mid-Air separation followed by separate flight. We investigate cooperative control strategies during joint flight that do not require any communication between the quadcopter and the biplane. This means that the two aircraft have their own independent control strategy based on their own sensors. The biplane, which is the largest of the two with most control authority, leads the flight and the goal for the quadrotor is to help in producing thrust and increasing rotational stability. Three control strategies for the quadrotor are compared: A proportional angular rate damper, a proportional angular acceleration damper, and constant thrust without attitude control. Simulation and practical tests show that for desired attitude changes of the biplane, the quadrotor rate-and angular acceleration damper strategies lead to a small performance degradation. However, the angular rate damper strategy reduces the roll angle error in disturbance rejection experiments and requires the smallest input command. The in-flight release is successfully tested in joint hover up to a forward pitch angle of-18.