基于逆投影的多椭圆联合快速高精度定位算法

doi:10.7527/S1000-6893.2022.27731

Abstract

Abstract:

Cooperative target measurement is an important positioning method for many kinds of operation tasks such as spacecraft rendering， docking， capture and maintenance. However， the current positioning method based on cooperative target has some problems， such as complex operation of target extraction and vulnerability to interferences， which result in poor timeliness， stability， and positioning accuracy. To solve the above problems， a location method of circular cooperative target is proposed based on inverse transformation of perspective projection. Firstly， target contour points are projected into the space by inverse projection of the imaging beam to form a plurality of elliptical cones composed of ray clusters. Then， an optimization model of position and posture residuals is constructed based on the relative relationship between multiple circular outlines of the cooperative target and elliptical conical ray clusters. Finally， an accurate pose of the target is obtained by the Levenberg-Marquadt algorithm. The measurement proposed does not need to fit the ellipse according to target contour points， which improves the calculation efficiency and avoids the accuracy error caused by ellipse fitting. The joint adjustment of multiple ray clusters greatly reduces the influence of noise and error points on position and posture accuracy， and improves the robustness and anti-interference of the algorithm. The experimental results show that the proposed algorithm has high accuracy， computing efficiency and robustness at different distances and noise environments， and can provide strong support for rapid， stable and accurate visual measurement of cooperative targets in the scenes of capture and rendezvous and docking of the space manipulator.

Key words: cooperative target, space robot, multiple circle target, space inverse projection, visual localization

CLC Number:

V448.2

Chuankai LIU, Junxiong LEI, Qian LIU, Jun SUN, Jianhua SU, Xiaodong HU, Dongsheng LI. Fast and precise location measurement of joint multiple ellipses based on inverse transformation of perspective projection[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(12): 327731-327731.

Figures/Tables 18

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输入	基于机械臂当前关节构型和基座位姿经正运动学结算得到末端相机初始迭代值 $Ω 0 = x 0, y 0, z 0, θ x 0, θ y 0, θ z 0 T$ 、常量 $β 、 σ ∈ 0,1$ ，当前迭代步数 $k = 0$ 、收敛阈值 $ε$ 取非常小的值， $s$ 表示 $Ω$ 的长度，即 $s = 6$ 。
步骤1	取 $Ω = Ω k$ 计算残差函数矩阵 $e k Ω k$ 及其雅可比矩阵 $J k Ω k$ 。
步骤2	计算 $g k = J k ⋅ e k$ ，如果 $n o r m g k ≤ ε$ ，迭代结束并返回 $Ω ̂ = Ω k$ ，否则进入步骤3。
步骤3	计算残差函数矩阵下降方向 $d k = - J k T ⋅ J k + m u k E s × s - 1 ⋅ g k$ ，其中 $m u k = n o r m e k$ 。
步骤4	采用Armijo算法线性搜索合适的下降步长 $h k$ ，满足 $e k Ω k + β ∧ h ⋅ d k ≤ e k Ω k + σ β ∧ h g k - 1 d k$ 的最小 $h$ 值。
步骤5	更新自变量 $Ω k + 1 = Ω k + β h k d k$ ，返回步骤2。
输出	末端相机精确位姿解 $Ω ̂$ 。

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Table 1

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Table 2

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圆形序号	半径/mm	x/mm	y/mm	z/mm	姿态角
1（外白色圆环）	18.75	-4.596	59.92	265	靶标姿态角均与适配器一致
1（内白色圆圈）	8	-56.073	59.92	265
2	9.32	-4.596	59.92	218.723
3	9.32	-4.596	134.585	257
4	9.32	-4.596	-14.745	257
5	9.32	-4.596	178.388	235
6	9.32	-4.596	93.73	235
7	9.32	-4.596	26.11	235
8	9.32	-4.596	-58.548	235

序号	耗时/ms
序号	本文算法	椭圆拟合+ Iterative迭代法	椭圆拟合+ EPNP算法
1	1.401	13.234	10.841
4	1.545	8.852	8.043
7	1.384	9.251	9.09
10	0.665	11.966	8.767
13	0.580	8.596	8.238
16	1.358	9.014	8.39

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Fast and precise location measurement of joint multiple ellipses based on inverse transformation of perspective projection

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