Experimental Study of Autonomous Target Pursuit with a Micro Fixed Wing Aircraft Stanley Ng, Frank Lanke Fu Tarimo, and Mac Schwager Mechanical Engineering Department, Boston University, Boston, MA, 02215 1 Motivation, Problem Statement, Related Work In this abstract we present a minimalist control strategy for a fixed wing Micro-Aerial Vehicle (MAV) to pursue a moving target in three dimensional space. The effectiveness of the control strategy is verified in numerous hardware experiments with a fixed wing MAV in a motion capture environment. Our approach is model free, in that it assumes no knowledge of the dynamics of the aircraft nor the target. The design is based on a well-known separation principle in aircraft dynamics, which allows the lateral and longitudinal dynamics to be treated independently with separate control designs [1]. The lateral mode is controlled with a Proportional Integral Derivative (PID) style architecture, while the longitudinal mode is controlled with a Proportional Integral (PI) architecture. Together, the controllers attempt to reduce the error between the aircraft s position and the target s position to zero. Additionally, the longitudinal controller incorporates a nonlinear term that is required to prevent adverse behavior in some flight regimes. We show in repeated experiments with a 3.6 gram modified Plantraco Carbon Butterfly in a motion capture environment, that this control strategy reliably pursues both fixed and moving targets (as shown in Fig. 1) over a range of initial conditions and target motions. Fig. 1. The 3.6 gram Carbon Butterfly is shown pursuing a static target on the left (represented by the hole in the box), and a dynamic target on the right (represented by the reflective marker at the end of the handheld wand). The objective of target pursuit [2] is for the pursuer to capture a target by moving sufficiently close to it (within a capture radius ). Much of the existing literature on controlling fixed wing MAVs deals with obstacle avoidance, trajectory following,
2 Ng, Tarimo, and Schwager navigation, or surveillance, however there is little existing work on target pursuit. Collision avoidance for MAVs has been investigated in numerous works. For example, in [3, 4] the authors use a custom vision sensor to control an MAV outdoors among obstacles and terrain. Collision avoidance with optical sensors is also considered in [5] where optical flow is used, and in [6], which uses stereo vision. Similarly, in indoor environments, [7] uses optical flow for collision avoidance, and [8] uses an on-board laser range finder for collision avoidance. Navigation and trajectory following for fixed wing MAVs have also been studied, for example in [9, 10], and more complex dynamical maneuvers such as perching were studied in [11]. Our work is different from all of these in that we do not seek to avoid obstacles or to follow a specific trajectory. Instead our objective is to pursue a target with the intent to capture it. This is somewhat similar to target tracking and surveillance, as in [12, 13], however the objective in these works is to best estimate the position of a target, not necessarily to capture it. Target pursuit algorithms for a simplified aircraft model were proposed and simulated in [14, 15], but with no experimental verification, as we provide in this work. 2 Technical Approach Our control design methodology is to separate the dynamical modes of the aircraft into lateral dynamics (incorporating roll angle, roll rate, yaw angle, yaw rate, and lateral velocity), and longitudinal dynamics (including pitch angle, pitch rate, forward velocity, upward velocity, and altitude). The Carbon Butterfly aircraft has only two control channels, rudder for lateral control, and throttle for longitudinal control. Our control designs for both of these are described below. Lateral Control The lateral controller is designed to steer the aircraft towards the target using the heading angle error. As shown in Fig. 2, the heading error e ψ = ψ d ψ c is the difference between the desired heading angle ψ d and the current heading ψ c. We compute the input to the rudder u r using a standard PID controller of the form Fig. 2. The heading angle error e ψ used to control the rudder position is shown graphically here. u r (t) = k P e ψ (t)+ k I e ψ (τ)dτ + k D ė ψ (t). Where k P, k I, and k D are control gains that are tuned by hand in our implementation. Longitudinal Control The longitudinal controller uses both the altitude error and the pitch angle error to produce a control input to the aircraft s throttle. The Carbon Butterfly aircraft has no elevator for independent pitch control, so pitch and altitude must be controlled together by changing the airspeed of the vehicle. The altitude error e z = z d z c is computed as the difference between the current altitude of the aircraft z c and the altitude of the target z d (which is the desired altitude of the aircraft). The pitch error is calculated as e θ = θ d θ c, where θ c is the current pitch angle, and θ d, the
Micro Fixed Wing Aircraft Pursuit 3 desired pitch angle, is set to zero since we intend to achieve level flight. These errors are used to control the throttle input u T with the PI control architecture u T (t) = k zp e z (τ) + k θp e θ (t) + k I e z (τ)dτ + k nl e z (t)e θ (t), where k zp, k θp, k I, and k nl are control gains that are tuned by hand. The nonlinear term e z (t)e θ (t) was found experimentally to prevent undesirable acceleration into the ground in certain flight regimes. The influence of this term can be seen by considering the sign of the resulting control signal in different regimes of the flight envelope, as shown in the left of Fig. 3. Specifically, when the pitch of the aircraft is too low and the altitude is below the target, the typical PI response is to increase throttle in order to increase altitude and pitch. Unfortunately this would tend to accelerate the aircraft into the ground. The nonlinear term prevents this effect, while having little impact under other flight conditions. Fig. 3. On the left, the effect of the nonlinear control term is shown in different regimes of the flight envelope. Most importantly, the nonlinear term prevents acceleration into the ground. On the right, the resetting mechanism of the integration term in shown, which prevents integrator wind-up. Furthermore, it was determined experimentally that the integral control term must be reset in certain flight regimes to prevent wind-up effects. 1 This is accomplished through a resetting strategy as follows. When the aircraft is lower in altitude than the target (e z > 0), and the aircraft s pitch angle is negative (e θ > 0), the integral term is reset to zero. Similarly, when the aircraft is higher in altitude than the target (e z < 0), the integral controller is also reset to zero. When the aircraft is flying below the target with zero pitch, the integral term results in throttle increase, as desired. The right plot in Fig. 3 shows these different regimes graphically. 3 Experiments Experiments were carried out using a Plantraco Carbon Butterfly RC model aircraft. The aircraft is 3.6 grams, with a 19cm wingspan. It has an integrated onboard RC re- 1 Integrator wind-up happens when the integration term becomes too large over time, dominating the other control terms.
4 Ng, Tarimo, and Schwager ceiver and motor driver board, driving a coil-actuated rudder for controlling roll and yaw, and a DC motor with a propeller for controlling speed, pitch, and altitude. The Carbon Butterfly lacks an elevator, making longitudinal control particularly challenging. Power is supplied with a custom miniature lithium-ion battery attached to the receiver board with magnetic contacts. We mounted hand-made reflective markers to the aircraft to track it in a OptiTrack motion capture environment. The heading error, altitude error, and pitch error were obtained in real-time from the OptiTrack system at a rate of 120Hz. The lateral and longitudinal controllers were implemented in MATLAB on a desktop computer, running in real time using these OptiTrack measurements. The computed control signals were then sent to the aircraft s RC transmitter using a buddy box functionality, and finally to the aircraft over the RC link, closing the control loop. The control gains were tuned by hand through extensive experimental trial and error in order to achieve repeatable, stable flight and traget pursuit from a range of initial positions and orientations. Fig. 4. The aircraft approaches the target from various points in the flight area. In the left frame, the initial lateral position is varied, and on the right the initial heading angle is varied. The figure above corresponds to a top-down view of the room. The plane approaches the target from various initial heights. The figure above corresponds to a side view of the flight area.
Micro Fixed Wing Aircraft Pursuit 5 4 Results The performance of the control system was tested with four different sets of experiments. For the first three sets of experiments, a target loop with a diameter of 60cm was placed 5m away from the aircraft. The aircraft was released by hand from a variety of initial configurations, and the goal was to determine the ability of the aircraft to fly through the target loop. The results of these three sets of experiments are shown in Fig. 4. The top two plots show the trajectories from a top view, while the bottom one Fig. 5. The plane here pursues a target mounted to a wand that is maneuvered by a human in the motion-capturing room. The trajectory of the aircraft is shown in blue, and that of the target is in red. in the video submitted with this abstract. show trajectories from a side view. The plot in the upper left shows a variety of initial lateral positions while keeping the same heading and altitude. The plot in the upper right shows a variety of initial heading angles, while keeping the same altitude and lateral position. These results indicate that the lateral controller is more robust to variations in initial lateral position than to variations in heading angle. The lower plot shows a variation in initial altitude while keeping the same lateral position and heading angle. It shows that the longitudinal controller is robust to a wide variation in initial altitude. For the fourth experiment, the aircraft was released by hand to track a moving traget. The target (designated by a trackable marker) was mounted to the end of a handheld wand and was freely maneuvered by a human. This experiment shows the tracking ability of the target pursuit controller. This is also illustrated 5 Main Experimental Insights In this project our intention was to design a control strategy for a complex dynamical system (an aircraft) to accomplish a complex task (target pursuit) through purely experimental means. The 7 different control gains (three for the lateral controller, and 4 for the longitudinal controller) were tuned by hand through extensive and repeated experimental trial and error. Indeed, the control architecture itself, particularly for the longitudinal controller was a product of experimental testing. An initial PID architecture was found to be unsuitable for the longitudinal mode, hence the derivative term was dropped, and the nonlinear term was added. Also, the integrator wind-up problem was observed experimentally, and was finally solved with the reset mechanism described in this paper. This experimental trial and error process produced a remarkably simple and robust control strategy to accomplish the complex control task of target pursuit with a
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