An In-Orbit Stereo Navigation Camera Self-Calibration Method for Planetary Rovers with Multiple Constraints

Abstract

In order to complete the high-precision calibration of the planetary rover navigation camera using limited initial data in-orbit, we proposed a joint adjustment model with additional multiple constraints. Specifically, a base model was first established based on the bundle adjustment model, second-order radial and tangential distortion parameters. Then, combining the constraints of collinearity, coplanarity, known distance and relative pose invariance, a joint adjustment model was constructed to realize the in orbit self-calibration of the navigation camera. Given the problem of directionality in line extraction of the solar panel due to large differences in the gradient amplitude, an adaptive brightness-weighted line extraction method was proposed. Lastly, the Levenberg-Marquardt algorithm for nonlinear least squares was used to obtain the optimal results. To verify the proposed method, field experiments and in-orbit experiments were carried out. The results suggested that the proposed method was more accurate than the self-calibration bundle adjustment method, CAHVOR method (a camera model used in machine vision for three-dimensional measurements), and vanishing points method. The average error for the flag of China and the optical solar reflector was only 1 mm and 0.7 mm, respectively. In addition, the proposed method has been implemented in China’s deep space exploration missions.

Current Status of the Community Sensor Model Standard for the Generation of Planetary Digital Terrain Models

“…This is essentially an implementation of a CAVHOR sensor model [42]. CAVHOR has been widely used in NASA's Mars rover missions and is described in Xu et al [43].…”

Three-Dimensional Reconstruction and Geometric Morphology Analysis of Lunar Small Craters within the Patrol Range of the Yutu-2 Rover

“…After the Yutu-2 lunar rover is launched and operating in orbit, the internal and external parameters of the camera calibrated on the ground may change. Therefore, to improve the accuracy of subsequent lunar terrain constructions, the present study employs the in-orbit self-calibration method of stereo cameras with additional multiple constraints [27] to accurately determine the internal and external parameters of the cameras. After a navigation camera captures a surround image, its field of view contains its solar panels (as shown in Figure 3).…”

“…where V 1 and V 2 are the image point residual corrections; V 3 is the correction of the 3D coordinates of the solar panel features; t 1 = [∆X l S , ∆Y l S , ∆Z l S , ∆φ l , ∆ω l , ∆κ l ] T and t 2 = [∆X r S , ∆Y r S , ∆Z r S , ∆φ r , ∆ω r , ∆κ r ] T are the corrections of the orientation elements inside the left and right images, respectively; X 1 = [∆x l 0 , ∆y l 0 , ∆ f l ] T and X 2 = [∆x r 0 , ∆y r 0 , ∆ f r ] T are the corrections of the inner orientation elements of the left and right images, respectively; X 3 = [∆X, ∆Y, ∆Z] T is the correction of the 3D coordinates of the solar panel features ; A, B, C, D, G, and F are the corresponding coefficient matrices; L l , L r , and L 3 are the residual matrices; P is the weight matrix corresponding to the observed quantity; and E is the identity matrix. Specific expressions for these parameters are provided in reference [27]. The least squares adjustment is applied to Equation (1) to obtain the substitution parameters (𝒕 𝟏 , 𝒕 𝟐 , 𝑿 𝟏 , and 𝑿 𝟐 ); the error in the unit weight is 0.210 pixels.…”

“…In the field of camera calibration, Zhang et al [26] proposed a method based on three-dimensional direct linear transformation (DLT) and multi-image rear intersection iterative computation for accurate lunar rover calibration. Xu et al [27] built a combined adjustment model for the self-calibrated beam method which includes distance constraints, collinearity and coplanarity conditions, and relative pose constraints of the stereo camera. With solar panels as calibration targets, after the rover landing, Yan et al [28] proposed using grid lines as a calibration method for linear parameters by applying the Hough transform, a clustering strategy, and least squares linear fitting.…”