Precise coordinated planning over a forward time window enables safe and
highly efficient motion when many robots must work together in tight spaces,
but this would normally require centralised control of all devices which is
difficult to scale. We demonstrate GBP Planning, a new purely distributed
technique based on Gaussian Belief Propagation for multi-robot planning
problems, formulated by a generic factor graph defining dynamics and collision
constraints over a forward time window. In simulations, we show that our method
allows high performance collaborative planning where robots are able to cross
each other in busy, intricate scenarios. They maintain shorter, quicker and
smoother trajectories than alternative distributed planning techniques even in
cases of communication failure. We encourage the reader to view the
accompanying video demonstration at this https URL.

本文提出了一种基于高斯信念传播的分布式技术 GBP Planning，用于解决多机器人规划问题，该方法可以在复杂的场景中实现高效的协作规划并保持短、快速、平滑的轨迹。

高斯置信度传播下的多机器人协作规划分配

Distributing Collaborative Multi-Robot Planning with Gaussian Belief Propagation

Graph processors such as Graphcore's Intelligence Processing Unit (IPU) are
part of the major new wave of novel computer architecture for AI, and have a
general design with massively parallel computation, distributed on-chip memory
and very high inter-core communication bandwidth which allows breakthrough
performance for message passing algorithms on arbitrary graphs. We show for the
first time that the classical computer vision problem of bundle adjustment (BA)
can be solved extremely fast on a graph processor using Gaussian Belief
Propagation. Our simple but fully parallel implementation uses the 1216 cores
on a single IPU chip to, for instance, solve a real BA problem with 125
keyframes and 1919 points in under 40ms, compared to 1450ms for the Ceres CPU
library. Further code optimisation will surely increase this difference on
static problems, but we argue that the real promise of graph processing is for
flexible in-place optimisation of general, dynamically changing factor graphs
representing Spatial AI problems. We give indications of this with experiments
showing the ability of GBP to efficiently solve incremental SLAM problems, and
deal with robust cost functions and different types of factors.

本文研究了基于 Graphcore 智能处理单元（IPU）的图处理器，证明了用高斯置信传播算法可以极快地解决经典计算机视觉问题中的束调整问题，并表明图处理的真正优势在于处理表示空间 AI 问题的一般动态因子图的灵活本地优化。

基于图处理器的束调整

Bundle Adjustment on a Graph Processor

The canonical problem of solving a system of linear equations arises in
numerous contexts in information theory, communication theory, and related
fields. In this contribution, we develop a solution based upon Gaussian belief
propagation (GaBP) that does not involve direct matrix inversion. The iterative
nature of our approach allows for a distributed message-passing implementation
of the solution algorithm. In the first part of this thesis, we address the
properties of the GaBP solver. We characterize the rate of convergence, enhance
its message-passing efficiency by introducing a broadcast version, discuss its
relation to classical solution methods including numerical examples. We present
a new method for forcing the GaBP algorithm to converge to the correct solution
for arbitrary column dependent matrices.
In the second part we give five applications to illustrate the applicability
of the GaBP algorithm to very large computer networks: Peer-to-Peer rating,
linear detection, distributed computation of support vector regression,
efficient computation of Kalman filter and distributed linear programming.
Using extensive simulations on up to 1,024 CPUs in parallel using IBM Bluegene
supercomputer we demonstrate the attractiveness and applicability of the GaBP
algorithm, using real network topologies with up to millions of nodes and
hundreds of millions of communication links. We further relate to several other
algorithms and explore their connection to the GaBP algorithm.

使用高斯信仰传递算法（GaBP）解决线性方程组问题，实现了迭代解法，从而实现了分布式消息传递实现解决方案的算法。通过广泛的模拟实验，在具有数百万节点和数亿通信链接的真实网络拓扑上展示了 GaBP 算法的吸引力和适用性。

高斯信念传播：理论与应用

Gaussian Belief Propagation: Theory and Aplication

We establish the convergence of the min-sum message passing algorithm for
minimization of a broad class of quadratic objective functions: those that
admit a convex decomposition. Our results also apply to the equivalent problem
of the convergence of Gaussian belief propagation.

该论文研究了在满足凸分解条件的广义二次目标函数下，最小 - 和消息传递算法的收敛性，同时也适用于高斯置信传播算法的收敛性问题。