流形上的集成规划与控制：因子图表示与工具包
Integrated Planning and Control on Manifolds: Factor Graph Representation and Toolkit
AI总结：
针对非线性流形系统上MPC的奇异性、收敛差等问题，提出基于因子图的FactorMPC工具包，原生支持流形值状态，设计流形上CBF避障因子，实现高维系统实时安全控制，四旋翼实验验证性能更优且开源可复现。
摘要：
模型预测控制（MPC）应用于在非线性流上演化的系统（如机器人姿态动力学和约束运动规划）时面临显著局限，传统欧几里得公式在这类场景中会遇到奇异性、过参数化和收敛性差的问题。为克服这些挑战，本文提出FactorMPC——一种基于因子图的MPC工具包，它将系统动力学、约束和目标统一到一个模块化、用户友好且高效的优化结构中。我们的方法原生支持流形值状态，并用切空间中建模的高斯不确定性来表征。通过利用因子图的稀疏性和概率结构，该工具包即使在具有复杂约束的高维系统中也能实现实时性能。我们设计了基于速度扩展的流形上控制屏障函数（CBF）的避障因子，适用于安全关键型应用。通过将图模型与安全关键型MPC相结合，我们的工作为集成规划与控制提供了一个可扩展且几何一致的框架。在四旋翼飞行器上的仿真和实验结果表明，与基线方法相比，该方法在轨迹跟踪和避障性能上更优。为促进研究可复现性，我们提供了开源实现，支持即插即用的因子。
英文摘要：
Model predictive control (MPC) faces significant limitations when applied to systems evolving on nonlinear manifolds, such as robotic attitude dynamics and constrained motion planning, where traditional Euclidean formulations struggle with singularities, over-parameterization, and poor convergence. To overcome these challenges, this paper introduces FactorMPC, a factor-graph based MPC toolkit that unifies system dynamics, constraints, and objectives into a modular, user-friendly, and efficient optimization structure. Our approach natively supports manifold-valued states with Gaussian uncertainties modeled in tangent spaces. By exploiting the sparsity and probabilistic structure of factor graphs, the toolkit achieves real-time performance even for high-dimensional systems with complex constraints. The velocity-extended on-manifold control barrier function (CBF)-based obstacle avoidance factors are designed for safety-critical applications. By bridging graphical models with safety-critical MPC, our work offers a scalable and geometrically consistent framework for integrated planning and control. The simulations and experimental results on the quadrotor demonstrate superior trajectory tracking and obstacle avoidance performance compared to baseline methods. To foster research reproducibility, we have provided open-source implementation offering plug-and-play factors.
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