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In this work we present a novel approach to recover objects 3D position and occupancy in a generic scene using only 2D object detections from multiple view images. The method reformulates the problem as the estimation of a quadric (ellipsoid) in 3D given a set of 2D ellipses fitted to the object detection bounding boxes in multiple views. We show that a closed-form solution exists in the dual-space using a minimum of three views while a solution with two views is possible through the use of non-linear optimisation and object constraints on the size of the object shape. In order to make the solution robust toward inaccurate bounding boxes, a likely occurrence in object detection methods, we introduce a data preconditioning technique and a non-linear refinement of the closed form solution based on implicit subspace constraints. Results on synthetic tests and on different real datasets, involving challenging scenarios, demonstrate the applicability and potential of our method in several realistic scenarios. [ABSTRACT FROM PUBLISHER]

This paper presents a new model-based algorithm that computes predictive optimal controls online and in a closed loop for traditionally challenging nonlinear systems. Examples demonstrate the same algorithm controlling hybrid impulsive, underactuated, and constrained systems using only high-level models and trajectory goals. Rather than iteratively optimizing finite horizon control sequences to minimize an objective, this paper derives a closed-form expression for individual control actions, i.e., control values that can be applied for short duration, that optimally improve a tracking objective over a long time horizon. Under mild assumptions, actions become linear feedback laws near equilibria that permit stability analysis and performance-based parameter selection. Globally, optimal actions are guaranteed existence and uniqueness. By sequencing these actions online, in receding horizon fashion, the proposed controller provides a min–max constrained response to a state that avoids the overhead typically required to impose control constraints. Benchmark examples show that the approach can avoid local minima and outperform nonlinear optimal controllers and recent case-specific methods in terms of tracking performance and at speeds that are orders of magnitude faster than traditionally achievable ones. [ABSTRACT FROM AUTHOR]