Terrain Mapping and Landing Operations Using Vision Based Navigation Systems

Majji, Manoranjan; Davis, Jeremy J.; Doebbler, James; Junkins, John L.; Macomber, Brent; Vavrina, Matthew A.; Vian, John

doi:10.2514/6.2011-6581

Cited by 14 publications

(5 citation statements)

References 17 publications

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“…The relationship in (33) parallels the SO(3) definition of [9] captured in (16); we have the product of the generating function and a (screw) axis. In the case that φ(ϕ) = ϕ, then ξ = ϕs is the familiar twist.…”

Section: Screws Pose Adjoints and Commutative Mappingsmentioning

confidence: 97%

“…3) Alternate Cayley Perturbation Solution: The previous section relied on using the infinitesimal expression for pose at each iteration. Here we take a slightly different strategy based on the Cayley transformation that is similar in spirit to that of [15,16,17,18,19,20]. We will refer to the resulting algorithm as CayPer.…”

Section: Pointcloud Alignmentmentioning

confidence: 99%

“…Here, we take a slightly different strategy based on the Cayley transformation that is similar in spirit to that of refs. [22][23][24][25][26][27]. We will refer to the resulting algorithm as CayPer.…”

Section: Alternate Cayley Perturbation Solutionmentioning

confidence: 99%

“…which requires only linear algebraic operations (e.g., no trigonometric functions). Notably, on the first iteration with T op = 1, the CayPer approach becomes a one-shot weighted optimal linear attitude and translation estimator [22][23][24][25][26][27] directly on SE (3). However, we can also continue to iterate to convergence of the original problem.…”

Section: Alternate Cayley Perturbation Solutionmentioning

confidence: 99%

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Vectorial parameterizations of pose

2021

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Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation – together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of a vector space are surjectively mapped to a matrix Lie group. For example, these vectorial representations can be employed for optimization as well as uncertainty representation on groups. The most common mapping is the matrix exponential, which maps elements of a Lie algebra onto the associated Lie group. However, this choice is not unique. It has been previously shown how to characterize all such vectorial parameterizations for SO(3), the group of rotations. Some results are also known for the group of poses, where it is possible to build a family of vectorial mappings that includes the matrix exponential as well as the Cayley transformation. We extend what is known for these pose mappings to the $4 \times 4$ representation common in robotics and also demonstrate three different examples of the proposed pose mappings: (i) pose interpolation, (ii) pose servoing control, and (iii) pose estimation in a pointcloud alignment problem. In the pointcloud alignment problem, our results lead to a new algorithm based on the Cayley transformation, which we call CayPer.

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Section: Screws Pose Adjoints and Commutative Mappingsmentioning

confidence: 97%

Section: Pointcloud Alignmentmentioning

confidence: 99%

Section: Alternate Cayley Perturbation Solutionmentioning

confidence: 99%

Section: Alternate Cayley Perturbation Solutionmentioning

confidence: 99%

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Vectorial parameterizations of pose

2021

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“…LiDAR sensors in particular, directly provide range measurements in the interest of landing/takeoff operations. However, LiDARs are prone to degradation of measurement density with range [10], [11]. Computing range rate from range measurements may lead to large errors and turn out to be unacceptable for precise landing environments.…”

Section: Introductionmentioning

confidence: 99%

An FPGA framework for Interferometric Vision-Based Navigation (iVisNav)

Bhaskara¹,

Sung²,

Majji³

2022

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Interferometric Vision-Based Navigation (iVisNav) is a novel optoelectronic sensor for autonomous proximity operations. iVisNav employs laser emitting structured beacons and precisely characterizes six degrees of freedom relative motion rates by measuring changes in the phase of the transmitted laser pulses. iVisNav's embedded package must efficiently process high frequency dynamics for robust sensing and estimation. A new embedded system for least squares-based rate estimation is developed in this paper. The resulting system is capable of interfacing with the photonics and implement the estimation algorithm in a field-programmable gate array. The embedded package is shown to be a hardware/software co-design handling estimation procedure using finite precision arithmetic for highspeed computation. The accuracy of the finite precision FPGA hardware design is compared with the floating-point software evaluation of the algorithm on MATLAB to benchmark its performance and statistical consistency with the error measures. Implementation results demonstrate the utility of FPGA computing capabilities for high-speed proximity navigation using iVisNav.

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