Traditionally rendezvous and proximity maneuvers have been performed using open-loop maneuver planning techniques and ad hoc error corrections. In this paper, a Model Predictive Control (MPC) approach is applied to spacecraft rendezvous and proximity maneuvering problems in the orbital plane. We demonstrate that various constraints arising in these maneuvers can be effectively handled with the MPC approach. These include constraints on thrust magnitude, constraints on spacecraft positioning within Line-of-Sight (LOS) cone while approaching the docking port on a target platform, and constraints on approach velocity to match the velocity of the docking port. The two cases of a non-rotating and a rotating (tumbling) platform are treated separately, and trajectories are evaluated in terms of maneuver time and fuel consumption. For the case when the platform is not rotating and the docking port position is fixed with respect to the chosen frame, an explicit off-line solution of the MPC optimization problem is shown to be possible; this explicit solution has a form of a piecewise affine control law suitable for on-line implementation without an onboard optimizer. In the case of a fast rotating platform, it is, however, shown that the prediction of the platform rotation is necessary to successfully accomplish the maneuvers and to reduce fuel consumption. Finally, the proposed approach is applied to debris avoidance maneuvers with the debris in the spacecraft rendezvous path. The significance of this paper is in demonstrating that Model Predictive Control can be an effective feedback control approach to satisfy various maneuver requirements, reduce fuel consumption, and provide robustness to disturbances. International Journal of Robust and Nonlinear ControlThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. SUMMARYTraditionally rendezvous and proximity maneuvers have been performed using open-loop maneuver planning techniques and ad hoc error corrections. In this paper, a Model Predictive Control (MPC) approach is applied to spacecraft rendezvous and proximity maneuvering problems in the orbital plane. We demonstrate that various constraints arising in these maneuvers can be effectively handled with the MPC approach. These include constraints on thrust magnitude, constraints on spacecraft positioning within Line-of-Sight (LOS) cone while approaching the docking port on a target platform, and ...

Many types of transformations are used to model deformations in medical image registration. While some focus on modeling local changes, some on continuity and invertibility, there is no closed-form nonlinear parametric approach that addresses all these properties. This paper presents a class of nonlinear transformations that are local, continuous and invertible under certain conditions. They are straightforward to implement, fast to compute and can be used particularly in cases where locally affine deformations need to be recovered. We use our new transformation model to demonstrate some results on synthetic images using a multi-scale approach to multi-modality mutual information based image registration. The original images were deformed using B-splines at three levels of scale. The results show that the proposed method can recover these deformations almost completely with very few iterations of a gradient based optimizer.

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