Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them to rank-1 matrices, a condition that can be challenging to achieve. In this work, we focus on trace-constrained SDPs (TCSDPs), where the decision variables are Positive Semi-Definite (PSD) matrices with fixed trace values. We show that the latter can be used to design a gradient-based refinement procedure that projects relaxed SDP solutions toward rank-1, low-cost candidates. We also provide fixed-trace SDP relaxations for common robotic quantities, such as rotations and translations, and a modular virtual robot abstraction that simplifies modeling across different problem settings. We demonstrate that our trace-constrained SDP framework can be applied to many robotics tasks, and we showcase its effectiveness through simulations in Perspective-n-Point (PnP) estimation, hand-eye calibration, and dual-robot system calibration.


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机器人(英语:Robot)包括一切模拟人类行为或思想与模拟其他生物的机械(如机器狗,机器猫等)。狭义上对机器人的定义还有很多分类法及争议,有些电脑程序甚至也被称为机器人。在当代工业中,机器人指能自动运行任务的人造机器设备,用以取代或协助人类工作,一般会是机电设备,由计算机程序或是电子电路控制。

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