LIDAR Assisted Rendezvous and Docking - Center for Space ...

USU LADARSIM Ladar Simulator• USU LADARSIM was developed forNAVAIR and incorporatesperformance-related parametersassociated with the laser, detector,signal processing, scannerdynamics, platform dynamics,navigation errors, and sceneproperties to provide generalsystem analysis, error sourcemodeling, and 3-D points clouds .Original Solid ModelRange Error14 cmNoiseless Point Cloud ModelNoisy Point Cloud Model

II I IZ point = R point -ptransZ pX py pR pointPx pointp transZ cIx pointy cX c

Complex singularitiesMean field assumption with singularity in the complex β plane:−∂P/∂β ∝ ln((1/β m − 1/β) 2 + Γ 2 ) ,Fisher zeros should stabilize at a distance Γβ 2 m from the real axis when thevolume increases.Large order behavior consistent with P(β) − P pert. (β) ≃ C(a/r 0 ) 4 , witha(β) defined with the force scale with r 0 = 0.5 fm.Bounds: 0.001 < Γ < 0.0113

Minimizing the Error Metric• The final step in the ICP algorithm was to compute an error metric that thealgorithm uses as a measure to the success of the calculated registrationfor each iteration.• For most applications, a mean square error (MSE) or sum of the squareddistance between corresponding points after the calculated registration wasapplied for point-to-point methods.MSE=1 N∑Ni=1vyi− R12vxi−vp122• Similarly, a MSE between corresponding points and matched planes can beused.NvMSE = n ⋅( A i− B i)∑i=1

Three-Axis Rotation Simulation ResultsPoint-to-Point vs Point-to-PointNo Noise NoisyThree Axis Rotation (º) (º)Maximum Mean Angular Error 1.79 2.54Minimum Mean Angular Error 1.46 1.85Average Mean Angular Error 1.69 2.211σ - Standard Deviatiation 1.32 1.82No Noise NoisyThree Axis Rotation (º) (º)Maximum Mean Angular Error 0.0546 0.8Minimum Mean Angular Error 0.0522 0.349Average Mean Angular Error 0.0532 0.4621σ - Standard Deviatiation 0.03 0.325

Three Axis Rotation:Error dependence on rotation anglePoint-to-Plane

Number of Points vs. Error and Computation Time

Conclusions• Completed testing of accelerated and robust version of the point-to-pointand point-to-plane ICP algorithm.• Implemented ICP/Point-Plane Algorithm– Significant accuracy improvement when compared to ICP/Point-Pointalgorithm• 14 cm error: 0.325º 1-σ error• 0 cm error: 0.037º 1-σ error– Currently analyzing more realistic 2 cm error conditions.– Incorporating translational correction algorithm– Initialization is way too slow for real-time work

Future Works and Tasks Underway• Investigating Real-Time initialization using Mach Filters, Spin Filters,or other possible options.• Preparing for experimental data recording and analysis fromCanesta system– Major data handling problem discovered and corrected• Modification of LadarSim to incorporate moving spacecraft