We present a framework for model-free batch localization and SLAM. We use lifting functions to map a control-affine system into a high-dimensional space, where both the process model and the measurement model are rendered bilinear. During training, we solve a least-squares problem using groundtruth data to compute the high-dimensional model matrices associated with the lifted system purely from data. At inference time, we solve for the unknown robot trajectory and landmarks through an optimization problem, where constraints are introduced to keep the solution on the manifold of the lifting functions. The problem is efficiently solved using a sequential quadratic program (SQP), where the complexity of an SQP iteration scales linearly with the number of timesteps. Our algorithms, called Reduced Constrained Koopman Linearization Localization (RCKL-Loc) and Reduced Constrained Koopman Linearization SLAM (RCKL-SLAM), are validated experimentally in simulation and on two datasets: one with an indoor mobile robot equipped with a laser rangefinder that measures range to cylindrical landmarks, and one on a golf cart equipped with RFID range sensors. We compare RCKL-Loc and RCKL-SLAM with classic model-based nonlinear batch estimation. While RCKL-Loc and RCKL-SLAM have similar performance compared to their model-based counterparts, they outperform the model-based approaches when the prior model is imperfect, showing the potential benefit of the proposed data-driven technique.

翻译：我们提出了一种无模型批处理定位与SLAM框架。通过提升函数将控制仿射系统映射到高维空间，使得过程模型与观测模型在该空间中均变为双线性形式。训练阶段，我们利用真实数据求解最小二乘问题，完全从数据中计算与提升系统对应的高维模型矩阵。推理阶段，通过优化问题求解未知的机器人轨迹与路标点，并引入约束以确保解位于提升函数的流形上。该问题通过序贯二次规划（SQP）高效求解，其中每次SQP迭代的计算复杂度随时间步数线性增长。本文算法称为降阶约束库普曼线性化定位（RCKL-Loc）与降阶约束库普曼线性化SLAM（RCKL-SLAM），并在仿真及两个数据集上进行了实验验证：其一涉及配备激光测距仪（测量圆柱形路标点距离）的室内移动机器人，其二则使用配备RFID测距传感器的高尔夫球车。我们将RCKL-Loc与RCKL-SLAM同经典基于模型的非线性批处理估计方法进行对比。尽管RCKL-Loc与RCKL-SLAM在性能上与基于模型的方法相当，但当前验模型存在不完美时，其性能优于基于模型的方法，展现了所提出数据驱动技术的潜在优势。