報(bào) 告 人：韓德仁 教授

報(bào)告題目：Non-convex Pose Graph Optimization in SLAM via Proximal Linearized Riemannian ADMM

報(bào)告時(shí)間：2024年11月4日(周一)上午9：30

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1508會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

       韓德仁，教授，博士生導(dǎo)師，現(xiàn)任北京航空航天大學(xué)數(shù)學(xué)科學(xué)學(xué)院院長(zhǎng)。從事大規(guī)模優(yōu)化問(wèn)題、變分不等式問(wèn)題的數(shù)值方法的研究工作，以及優(yōu)化和變分不等式問(wèn)題在交通規(guī)劃、磁共振成像中的應(yīng)用，發(fā)表多篇學(xué)術(shù)論文。曾獲中國(guó)運(yùn)籌學(xué)會(huì)青年科技獎(jiǎng)，江蘇省科學(xué)技術(shù)獎(jiǎng)等獎(jiǎng)項(xiàng)；主持國(guó)家自然科學(xué)基金杰出青年基金項(xiàng)目、重點(diǎn)項(xiàng)目等。擔(dān)任中國(guó)運(yùn)籌學(xué)會(huì)常務(wù)理事；《數(shù)值計(jì)算與計(jì)算機(jī)應(yīng)用》、《Journal of the Operations Research Society of China》、《Journal of Global Optimization》、《Asia-Pacific Journal of Operational Research》編委。

報(bào)告摘要：

       Pose graph optimization (PGO) is a well-known technique for solving the pose-based simultaneous localization and mapping (SLAM) problem. In this paper, we represent the rotation and translation by a unit quaternion and a three-dimensional vector, and propose a new PGO model based on the von Mises-Fisher distribution. The constraints derived from the unit quaternions are spherical manifolds, and the projection onto the constraints can be calculated by normalization. Then a proximal linearized Riemannian alternating direction method of multipliers (PieADMM) is developed to solve the proposed model, which not only has low memory requirements, but also can update the poses in parallel. Furthermore, we establish the iteration complexity of O(1/ε2) of PieADMM for finding an ?-stationary solution of our model. The efficiency of our proposed algorithm is demonstrated by numerical experiments on two synthetic and four 3D SLAM benchmark datasets.