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SCIENCE CHINA Information Sciences, Volume 64 , Issue 7 : 172209(2021) https://doi.org/10.1007/s11432-020-3056-5

Smooth quadrotor trajectory generation for tracking a moving target in cluttered environments

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  • ReceivedJun 2, 2020
  • AcceptedSep 1, 2020
  • PublishedMay 20, 2021

Abstract


Acknowledgment

This work was supported by the Key Program of National Natural Science Foundation of China (NSFC) (Grant No. U1613225). The authors would like to thank Unmanned System Research Groups at the Chinese University of Hong Kong (CUHK) and Peng Cheng Laboratory (PCL) at Shenzhen, China.


References

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  • Figure 1

    (Color online) A scenario of target tracking.

  • Figure 2

    The framework of proposed method.

  • Figure 5

    (Color online) The illustration of an SFC. (a) The scene diagram of SFC; (b) closed convex polytopes ${\rm~SFC}_i$. In (a), The path found by the nominal path-finding algorithm is shown as green grids. The flight corridor is marked in yellow. The dash black circle and solid red square respectively represent the sphere obtained by position from the node to nearest obstacle and the cube inscribed the sphere.

  • Figure 6

    (Color online) The illustration of constraint volume. The gray cylinder represents the volume expressed by Eqs. (19) and (20) while the red volume is the embedded cuboid of cylinder.

  • Figure 7

    (Color online) Trajectory generation results in complex environment. (a) Trajectory generation in complex environment; (b) velocity; (c) acceleration.

  • Figure 8

    (Color online) Trajectory generation results in narrow corridor. The green dots are the waypoints to approximate or pass through. (a) 2D illustration; (b) Euclidean distance map illustration.

  • Figure 9

    (Color online) Results of finding feasible waypoints in two different tracking patterns.

  • Figure 10

    (Color online) Trajectory generation results of tracking a moving target in relative tracking pattern in narrow corridor. The red pluses represent waypoints of moving target while the blue stars are the corresponding waypoints of the quadrotor calculated by Subsection 3.1.1. (a) $t=2.0$ s; (b) $t=4.0$ s; (c) $t=6.0$ s; (d) $t=8.0$ s; (e) $t=10.0$ s.

  • Figure 11

    (Color online) The planned velocities and accelerations when the quadrotor tracks a moving target in relative tracking pattern in narrow corridor. (a) Velocity; (b) acceleration.

  • Figure 12

    (Color online) Trajectory generation results of tracking a moving target in relative tracking pattern in complex environment. (a) Trajectory; (b) velocity; (c) acceleration.

  • Figure 13

    (Color online) Trajectory generation results of tracking a moving target in visibility maintenance pattern in narrow corridor. The red pluses represent waypoints of moving target while the blue stars are the corresponding waypoints obtained by trading off the flight length and visibility. The red sector represents the FOV. (a) $t=2.0$ s; (b) $t=4.0$ s; (c) $t=6.0$ s;protectłinebreak (d) $t=8.0$ s; (e) $t=10.0$ s.

  • Figure 14

    (Color online) The planned velocities and accelerations when the quadrotor tracks a moving target in visibility maintenance pattern in narrow corridor. (a) Velocity; (b) acceleration.

  • Figure 15

    (Color online) Trajectory generation results of tracking a moving target in visibility maintenance pattern in complex environment. (a) Trajectory; (b) velocity; (c) acceleration.

  • Table 1  

    Table 1Time cost of trajectory generation in complex environment

    Method Snap cost Time cost (ms)
    B-spline 22.72 33.2
    Polynomial 45.68 26.4
  •   

    Algorithm 1 Safe flight corridor generation

    Require:Map, waypoints.

    Output:SFC.

    Generate path from current position to waypoints;

    for each node of path

    Find distance $d_s$ to the nearest obstacle;

    Generate initial sphere and inscribed cube based on $d_s$;

    Enlarge cube until it hits an obstacle;

    end for

    Generate initial ${\rm~SFC}_{\rm~initial}$ with enlarged cubes;

    $m$ = size(cubes);

    for $i=m:2$

    for $j=m-1:1$

    if ${\rm~cube}_j$ is contained by ${\rm~cube}_i$ then

    Eliminate ${\rm~cube}_j$;ELSIF ${\rm~cube}_i$ is contained by ${\rm~cube}_j$

    Eliminate ${\rm~cube}_i$;

    end if

    end for

    end for

    $n$ = size(cubes);

    for $i=n:3$

    for $j=n-2:1$

    if ${\rm~cube}_i$ overlap with ${\rm~cube}_j$ then

    Eliminate ${\rm~cube}_{j+1}$, $~\dots$, ${\rm~cube}_{i-1}~$;

    end if

    end for

    end for

  •   

    Algorithm 2 The sequential planning

    Require:Cost function $J$, waypoints $W(t_f)$.

    Output:$C$, control point matrix of spline trajectory.

    for each planning horizon

    Update the waypoints $W(t_f)$;

    Generate SFC;

    $C~\leftarrow~{\rm~iterateQP}(J,C,W(t_f))$;

    Return $C$;

    end for

  • Table 2  

    Table 2Snap cost of trajectory generation in narrow corridor

    Method Snap cost
    Proposed method 48.40
    Contouring planning method 76.20
  • Table 3  

    Table 3Parameter configurations

    Parameter Value (narrow corridor) Value (complex environment)
    $d_h$ 2.0 m 2.0 m
    $d_v$ 3.0 m 2.0 m
    $\theta$ $\pi/4$ $\pi/3$
    $\lambda$ 100 100
  • Table 4  

    Table 4Average time cost

    Process Time cost (ms)
    Path planning 8.2
    Waypoint found 1.8
    SFC generation 18.6
    Trajectory generation 6.8
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