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We present new extensions of the two-step, triangular-pattern phase-shifting method for different numbers of phase-shifting steps to increase measurement accuracy and to analyze the influence of the number of phase-shifting steps and pitch of the projected triangular intensity-profile pattern on the measurement accuracy. Phase-shifting algorithms to generate the intensity ratio, essential for surface reconstruction, were developed for each measurement method. Experiments determined that higher measurement accuracy can be obtained with a greater number of phase-shifting steps and a lower value of pitch, as long as the pitch is appropriately selected to be divisible by the number of phase-shifting steps and not below an optimal value, where intensity-ratio unwrapping failure would occur.

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This paper presents a fault-tolerant method for pose estimation of space objects using 3-D vision data by integration of a Kalman filter (KF) and an Iterative Closest Point (ICP) algorithm in a closed-loop configuration. The initial guess for the internal ICP iteration is provided by state estimate propagation of the Kalman filer. The Kalman filter is capable of not only estimating the target's states, but also its inertial parameters. This allows the motion of target to be predictable as soon as the filter converges. Consequently, the ICP can maintain pose tracking over a wider range of velocity due to increased precision of ICP initialization. Furthermore, incorporation of the target's dynamics model in the estimation process allows the estimator continuously provide pose estimation even when the sensor temporally loses its signal namely due to obstruction. The capabilities of the pose estimation methodology is demonstrated by a ground testbed for Automated Rendezvous & Docking (AR&D). In this experiment, Neptec's Laser Camera System (LCS) is used for real-time scanning of a satellite model attached to a manipulator arm, which is driven by a simulator according to orbital and attitude dynamics. The results showed that robust tracking of the free-floating tumbling satellite can be achieved only if the Kalman filter and ICP are in closed-loop configuration.

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