vol1is1pp2
Journal of Unmanned System Technology
LP Based Path Planning for Autonomous Landing of An Unmanned Helicopter on A Moving Platform
Chong Wu^{†‡}, Juntong Qi^{†}, Dalei Song^{†}, and Jianda Han^{†}
^{†}State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016
^{‡}University of Chinese Academy of Sciences, Beijing 100049, P.R. China.
Abstract— Autonomous landing of an unmanned helicopter (UH) on a moving platform can greatly expand its application field. In this paper, a path planning method based on linear programming (LP) is proposed in the relative coordination to finish the autonomous landing task. First, the landing procedure is divided into four stages. Then, the linear constraints in each stage are established respectively which include helicopter’s flight envelope constraints and target kinematic constraints. Based on the established LP formulations, the flight control system’s optimal velocity expectation is derived. A simulation system based on FlightGear and Matlab is established and used as the validation platform for this approach, the simulation results demonstrate the effectiveness and efficiency of this approach and the real flight test is under development.
Keywords— autonomous landing, LP, moving platform, UH
I. INTRODUCTION
Autonomous landing is a crucial capability for an UH to finish any mission. In [1], a real time vision system is built up based on a cooperative landing target, the image processing algorithm could be greatly simplified and accuracy of the location is greatly increased. The accuracy of this vision system is within 40cm in position and 7 degree in orientation. Autonomous landing is finished using the behaviorbased controller by following a path to the landing site based on the landing parameters derived from the vision system. In [2], a different vision cooperative landing target is proposed and verified in flight test with the accuracy up to 5cm in position and 5 degree in orientation, the landing task is finished in a different control framework as a hierarchical flight management system. In [13], a lidarbased landing zone perception system is built for autonomous landing of a fullscale helicopter at unprepared sites. These researches mainly focus on the navigation system to derive a more accurate and stable relative position and orientation information between the UH and the landing site which is assumed to be stationary. In [3], tether is used to guide landing of UHs on a rocking ship deck, at the same time the tether tension is used to couple the translation of the UH to the rotation, two controllers are developed for faraway and near ship control, the main focus is on the stability of the proposed controller. In [4], a predictor is built up to estimate the movement of ship deck’s altitude, and a feedbackfeedforward controller is proposed based on the estimation of the wind disturbance to obtain more stable altitude control accuracy. These researches mainly focus on the stability of autonomous landing controller as the flight condition is different compared with the groundbased stationary landing.
As what has been reviewed in the preparagraph, currently the researches in autonomous landing mainly focus on navigation accuracy and controller stability, but seldom devote to the path planning for autonomous landing especially autonomous landing on a moving platform. While the landing on a moving platform can greatly expand the application field of UHs, for example, the autonomous landing on a moving ship can be of significant importance for shipboard applications since the main difference and challenge for UHs in shipboard applications compared with landbased applications is takeoff and landing. Compared with stationary landing, autonomous landing on a moving platform proposes more challenge on path planning because the strategy and method of path planning will directly decide the safety of autonomous landing.
Path planning for autonomous vehicles in three dimensional spaces to catch moving targets while avoiding obstacles in sensoreffective range is a challenging problem, especially when realtime is demanded in timevarying environment [5]. Mathematical programming methods treat the trajectory planning problem as a numerical optimization problem. However, the cost functions typically have a number of local minima [10]; a proper selection of cost function is the most key factor for the implementation of mathematical programming methods. Linear programming (LP) is a general tool for optimization with the capability satisfying performance criterion and dynamic constraints. The path derived using either LP or mixed integer LP (MILP) ([7],[8]) is optimal with respect to an objective function while satisfying multiple constraints. However, it is difficult for MILP to be used as a real time path planner due to its computational complexity, and this is especially difficult when there are multiple moving obstacles with irregular contours [5]. In [6], the task of targetpursuit and obstacleavoidance is modeled with linear constraints in relative coordination according to LP formulation, and two cost functions are integrated into the objective function of LP for obstacleavoidance and targetpursuit respectively. Compared with ant colony optimization algorithm [9] and genetic algorithm [11], LP method has less parameter to tune and can achieve better performance in realtime application [6].
Tremendous progress has been made to increase the UHs’ intelligence in Shenyang Institute of Automation Chinese Academy of Sciences before [14]–[19]. In this paper, LP is adopted for path planning of autonomous landing of a UH on a moving platform. First, the landing procedure is divided into four stages. Then, the linear constraints in each stage are established accordingly which include helicopter’s flight envelope constraint and target kinematical constraint. Autonomous landing of an UH on a stationary platform, a moving platform and a moving ship have been realized respectively based on the proposed path planning method and the established hardware in the loop simulation system.
II. Statement of landing Problem
Autonomous landing of an UH on a moving platform specified in this paper is defined as follow: As the platform moving on the ground with its lateral and longitudinal movement and attitudes vibration to simulate the movement of ship on the sea, the UH tries to follow the horizontal movement of at a safe altitude above the platform and at a proper time decrease its altitude to land on with minimum attitude deviation, minimum position deviation and minimum relative velocity deviation in each axis to avoid strong shock and guarantee the safety of both UH and platform.
Generally, the autonomous landing procedure can be divided into four stages [2]:
Figure 1 Autonomous landing strategy
1. Landing target searching
As the helicopter starts the autonomous landing procedure, landing target should be specified first. In this paper, we assume the target’s information is preknown and this stage can be ignored.
2. Target pursuit
The target is assumed to move on the ground with zero height; the initial altitude of UH would above the ground. Strategy for safe landing is to track the movement at a safe pursuit altitude and minimize the horizontal position deviation first. Pursuit at a safe altitude is requisite since flying at a low altitude will encounter more obstacles which would endanger the safety of UH.
3. Initial descent
If the UH has moved near the target with a proper horizontal position deviation, with the assumption that no obstacles exist above the landing zone, the UH will decrease its altitude to a safe landing altitude above the deck. This initial descent is to provide a period for landing deck verification and movement prediction.
4. Final descent
When the UH has finished the initial descent and safe landing has verified, final descent would execute to land on the deck at a minimum relative velocity in each axis and minimum position deviation in each axis.
III. LP Formulation
All the symbols and variables mentioned following are listed in Table 1. Assumptions for landing are list as follow [6]:
· The target’s acceleration is assumed to be zero in the planning period. Since the planning period is short enough and the target’s movement changes very slowly, this assumption can be satisfied generally. With this assumption, we have: .
· The target’s velocity won’t exceed the maximum velocity of helicopter; this will guarantee that the helicopter can catch up and land on the target finally.
The coordinates used in this paper are defined as shown in Figure 2, with the helicopter bodyfix reference frame, the moving target bodyfix reference frame, the inertial reference frame.
Figure 2 Coordinates definition
Table 1 Nomenclature

Helicopter, target 

Planning period 

Helicopter velocity in 

Target velocity in 

Relative velocity 

Relative position 

Temporal variable 

Helicopter acceleration 

Relative acceleration 

Angle between horizontal relative velocity and horizontal position 

Auxiliary variable 

Magnitude of corresponding vector 

xy component of corresponding vector 
LP formulations for target pursuit are separated into horizontal position pursuit, yaw pursuit and altitude position pursuit respectively. In different land stages, different planning strategies will be employed based on the combination of these formulations.
A. Horizontal position pursuit
With the horizontal relative velocity and its orthogonal component .. and depicted in Figure 3, the policy for the optimal velocity in horizontal is defined as following:
Figure 3 Horizontal relative velocity and orthogonal components and
Considering the dynamic constraints of the UH, we have following constraints:
1) Velocity constraint
Since the projecting plane of the lateral airframe is much wider compared with the longitudinal airframe, wind resistance exerts on lateral movement would be bigger which results in a less maximum lateral velocity. The maximum velocity is different in lateral and longitudinal axis, generally used simplification such as a unified square or circle can’t satisfy the requirement, here we assume the helicopter’s velocity satisfy the constraint as an ellipse:
whereand are the longitudinal and lateral velocity of UH respectively, and are the maximum velocity in longitudinal and lateral axis respectively. Generally, would be half of.
Multiplanes are used to approximate the ellipse constraints of velocity as shown in to satisfy the linear constraint requirement of LP.
where
2) Acceleration constraint
The feasible region of helicopter’s acceleration is as follow. Like , multiplanes [6] are used to approximate the constraints of acceleration.
where .
According to [6], we have the optimization rule as following:
B. Yaw pursuit
As what has been stated in velocity constraint, lateral maximum velocity and longitudinal velocity is different. Then the optimal yaw is to align the helicopter with the under the constraint of the maximum yaw rate limitation.
where is the yaw of helicopter, is the maximum yaw rate of helicopter.
Actually, yaw pursuit is only required when the helicopter is far away from the target. As the helicopter near the target, velocity in any axis can track the movement of target and yaw pursuit is of no sense anymore.
C. Altitude pursuit
Altitude pursuit has its special requirement: compared with the horizontal pursuit, relative vertical velocity must be minimized to avoid the landing accident. A balance should be made between the relative altitude deviation and the relative vertical velocity. Here target is assumed to be on the ground without vertical movement, this will simplify the problem, and we have the LP formulation as following:
where is the weight factor which will make a balance between the altitude bias and relative touching velocity, and is selected in accordance with the maximum decent velocity defined in autonomous landing.
IV. Simulation and Result
A hardwareintheloop (HIL) simulation and test platform has been developed for algorithms simulation and validation [12]. The simulation system includes a 3D flight and scenery simulator, a flight control system, a ground control station, and a RC pilot controller. Based on a semidecoupled flight dynamic model, which is acquired from a frequency domain system identification method using real flight hovering data, an autonomous PID controller is implemented and verified in both simulation and real flight tests. The simulation system is shown in Figure 4. An extra computer is utilized to simulate movement of the moving target and send target’s information to the flight controller for path planning. LP solver for path planning is realized on a computer and the path planning result is then sends to the flight controller. The architecture of the overall simulation system is as shown in Figure 5.
Figure 4 Simulation system
Figure 5 Simulation system architecture
Three simulations are conducted: first we demonstrate the autonomous landing on a stationary platform, and then landing on a moving platform is further demonstrated, autonomous landing a moving ship is conducted finally to validate the overall system and the effectiveness of the proposed algorithms.
The UH dynamic constraints and parameters for simulation are listed in Table 2. These constraints and parameters are the real value specified by the UH we developed as Servoheli40.
Table 2 Dynamic constraints and parameters






20 m/s 
10 m/s 
3 m/s^{2} 
0.5 s 
3 m/s 
1 m/s^{2} 
A. Landing on a stationary platform
In this simulation, the landing target is assumed to be at a fix point without movement; the helicopter hovering at an initial position is expected to move to and land on the target. States for simulation are listed in Table 3.
Table 3 States for Stationary landing






(300, 250, 0) 
(0, 0, 50) 
(0, 0, 0) 
(0, 0, 0) 
(0, 0, 0) 
0 
Figure 6 shows the path planning result for the stationary landing. A comparison is made between the fix yaw pursuit and the pursuit with yaw dynamically aligned with the target. As the Figure 6showing, they have almost the same flying pursuit trace. The black arrow in the figure is the yaw of the UH, as we can see, the yaw will finally aligned with the target. But as shown in Figure 7, the velocity in xaxis is different; a maximum pursuit velocity can be reached which decreases the landing period from 1180 steps to 799 steps. This result demonstrates the validity of the necessity of dynamic yaw alignment and the effectivity of the whole landing strategy.
Figure 6 Stationary landing: flying trace at vertical view, black arrows represent yaw of the UH
Figure 7 Stationary landing: flying velocity in xaxis
B. Landing on a moving platform
In this simulation, the target is moving at a speed of (3,5,0) first and then the speed changes to (5,1,0) at time step 300, States for simulation are listed in Table 4.
Table 4 States for Moving Platform Landing






(300, 250, 0) 
(0, 0, 50) 
(0, 0, 0) 
(3, 5, 0) 
(0, 0, 0) 
0 



(5, 1, 0) as k>300 


The pursuit trace is shown in Figure 8, as we can see, even with a sudden velocity change, the helicopter can finish the pursuit and landing. Figure 9 is the altitude deviation and vertical velocity, this implies that the helicopter can landing on the target with almost zero relative vertical velocity to minimize the shock of landing.
Figure 8 Landing on a moving platform: flying trace vertical view, black arrows represent yaw of the UH
Figure 9 Landing on a moving platform: altitude deviation and vertical velocity
C. Landing on a moving ship
To validate the proposed algorithm and the simulation system, here a simulation of an UH autonomously landing on a moving ship is conducted. In the simulation, the UH is supposed to track a moving ship and land on it properly.
A simplified ship dynamic model is used to simulate the movement of a real ship; the model is list as following:
where and are the position in north and east coordination respectively, and are the orientation and yaw rate, and are the velocity in body axis, and are the control input. The parameters of ship are listed as following:
The simulation result is shown in Figure 10 and Figure 11. As shown in Figure 10, as the UH start landing procedure, it will follow the predefined procedure: target pursuit, initial descent, final descent, landing on the ship. The UH can autonomous track and land on the ship with the predefined strategy.
Figure 10 Landing on a moving ship: trace of the UH and the ship
Figure 11 Screen shot of landing on a moving ship
V. Conclusion
With the proposed strategy for autonomous landing of an unmanned helicopter on a moving platform, this paper established a path planning algorithm based on LP method. Incorporating the UH dynamic constraints and flight envelop constraints, LP formulations for horizontal pursuit, yaw pursuit and vertical pursuit have been established respectively. A hardwareintheloop simulation and test platform has been established based on Matlab and FlightGear for algorithms validation purpose, further investigation on flight controller design and path planning can also be conducted on this platform. Autonomous landing of an UH on a stationary platform, a moving platform and a moving ship have been realized based on the proposed path planning algorithms and the established simulation platform. The simulation results demonstrate that with the proposed algorithm the UH can successfully pursuit and land on a moving target with a safe landing strategy and safe relative touching velocity.
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