SLAM技术的演变与未来：迈向鲁棒感知时代
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"SLAM（Simultaneous Localization And Mapping，同时定位与建图）是机器人领域的一个核心问题，本文深入探讨了SLAM的发展历程，并展望了其未来趋势。文章由C.Cadena、L.Carlone、H.Carrillo、Y.Latif、D.Scaramuzza、J.Neira、I.Reid和J.J.Leonard共同撰写，发表在2016年的IEEE Transactions on Robotics期刊上，页码为1309-1332，卷号32，编号6。"
SLAM是机器人技术中的一个关键挑战，它涉及机器人在未知环境中的自主导航和地图构建。这个过程允许机器人同时估计自身的位置和环境的结构。SLAM的研究始于上世纪80年代末，随着机器人和自动化领域的进步，SLAM技术也经历了多个发展阶段。
早期的SLAM方法主要依赖于手工特征，如边缘、角点等，通过匹配这些特征来实现定位和建图。然而，这种方法容易受到光照变化、遮挡和重复纹理的影响。随后，研究者引入了滤波理论，如扩展卡尔曼滤波（EKF）和粒子滤波（PF），来处理SLAM问题中的不确定性。这些滤波方法在一定程度上提高了SLAM的性能，但仍然存在计算复杂度高和难以处理非线性问题的局限。
近年来，随着视觉传感器的发展，视觉SLAM（Visual SLAM，VSLAM）成为研究热点。VSLAM利用相机捕获的图像序列，通过特征匹配和几何验证来估计位姿和构建环境的稠密或稀疏地图。比如，ORB-SLAM和PTAM等系统就是视觉SLAM的典型代表，它们在实时性能和鲁棒性上取得了显著进步。
与此同时，随着深度学习的兴起，数据驱动的方法开始被应用于SLAM，尤其是基于深度神经网络的端到端学习SLAM。这些方法试图直接从原始传感器数据中学习位姿估计和建图，从而避免手动特征提取和复杂的数学模型。尽管这些方法在某些场景下表现优秀，但它们的可解释性和泛化能力仍然是当前研究的重点。
SLAM的未来发展趋势包括但不限于以下几个方面：
1. **鲁棒性增强**：提高SLAM在动态环境、光照变化、传感器噪声等复杂条件下的稳定性。
2. **实时性和效率**：优化算法以适应更高速度的传感器数据流，同时降低计算资源的需求。
3. **多模态融合**：结合多种传感器数据（如激光雷达、IMU、视觉等）以提高定位精度和环境理解能力。
4. **深度学习集成**：将深度学习与传统SLAM框架结合，以提升系统性能和自适应能力。
5. **三维重建**：发展更高效、精确的三维重建技术，支持大规模、高精度的环境建模。
6. **应用拓展**：SLAM技术将进一步应用于自动驾驶、无人机、增强现实（AR）、虚拟现实（VR）等领域。
SLAM作为机器人技术的核心组成部分，其发展历程展示了从基础理论到实际应用的不断演进。随着技术的进步，SLAM在未来有望实现更智能、更可靠的自主导航和环境感知，推动我们进入一个强大的感知时代。
4
Maximum a posteriori (MAP) estimation and the SLAM
back-end. The current de-facto standard formulation of SLAM
has its origins in the seminal paper of Lu and Milios [161],
followed by the work of Gutmann and Konolige [101].
Since then, numerous approaches have improved the efficiency
and robustness of the optimization underlying the problem
[63, 81, 100, 125, 192, 241]. All these approaches formulate
SLAM as a maximum a posteriori estimation problem, and
often use the formalism of factor graphs [143] to reason about
the interdependence among variables.
Assume that we want to estimate an unknown variable X ; as
mentioned before, in SLAM the variable X typically includes
the trajectory of the robot (as a discrete set of poses) and
the position of landmarks in the environment. We are given
a set of measurements Z = {z
k
: k = 1, . . . , m} such that
each measurement can be expressed as a function of X , i.e.,
z
k
= h
k
(X
k
)+
k
, where X
k
⊆ X is a subset of the variables,
h
k
(·) is a known function (the measurement or observation
model), and
k
is random measurement noise.
In MAP estimation, we estimate X by computing the
assignment of variables X
?
that attains the maximum of the
posterior p(X |Z) (the belief over X given the measurements):
X
?
.
= argmax
X
p(X |Z) = argmax
X
p(Z|X )p(X ) (1)
where the equality follows from the Bayes theorem. In (1),
p(Z|X ) is the likelihood of the measurements Z given the
assignment X , and p(X ) is a prior probability over X . The
prior probability includes any prior knowledge about X ; in
case no prior knowledge is available, p(X ) becomes a constant
(uniform distribution) which is inconsequential and can be
dropped from the optimization. In that case MAP estimation
reduces to maximum likelihood estimation. Note that, unlike
Kalman filtering, MAP estimation does not require an explicit
distinction between motion and observation model: both mod-
els are treated as factors and are seamlessly incorporated in the
estimation process. Moreover, it is worth noting that Kalman
filtering and MAP estimation return the same estimate in the
linear Gaussian case, while this is not the case in general.
Assuming that the measurements Z are independent (i.e.,
the corresponding noises are uncorrelated), problem (1) fac-
torizes into:
X
?
= argmax
X
p(X )
m
Y
k=1
p(z
k
|X ) =
argmax
X
p(X )
m
Y
k=1
p(z
k
|X
k
) (2)
where, on the right-hand-side, we noticed that z
k
only depends
on the subset of variables in X
k
.
Problem (2) can be interpreted in terms of inference over a
factors graph [143]. The variables correspond to nodes in the
factor graph. The terms p(z
k
|X
k
) and the prior p(X ) are called
factors, and they encode probabilistic constraints over a subset
of nodes. A factor graph is a graphical model that encodes
the dependence between the k-th factor (and its measurement
z
k
) and the corresponding variables X
k
. A first advantage of
the factor graph interpretation is that it enables an insightful
Fig. 3: SLAM as a factor graph: Blue circles denote robot poses at
consecutive time steps (x
1
, x
2
, . . .), green circles denote landmark positions
(l
1
, l
2
, . . .), red circle denotes the variable associated with the intrinsic
calibration parameters (K). Factors are shown as black squares: the label
“u” marks factors corresponding to odometry constraints, “v” marks factors
corresponding to camera observations, “c” denotes loop closures, and “p”
denotes prior factors.
visualization of the problem. Fig. 3 shows an example of a
factor graph underlying a simple SLAM problem. The figure
shows the variables, namely, the robot poses, the landmark
positions, and the camera calibration parameters, and the
factors imposing constraints among these variables. A second
advantage is generality: a factor graph can model complex
inference problems with heterogeneous variables and factors,
and arbitrary interconnections. Furthermore, the connectivity
of the factor graph in turn influences the sparsity of the
resulting SLAM problem as discussed below.
In order to write (2) in a more explicit form, assume that
the measurement noise
k
is a zero-mean Gaussian noise with
information matrix Ω
k
(inverse of the covariance matrix).
Then, the measurement likelihood in (2) becomes:
p(z
k
|X
k
) ∝ exp(−
1
2
||h
k
(X
k
) − z
k
||
2
Ω
k
) (3)
where we use the notation ||e||
2
Ω
= e
T
Ωe. Similarly, assume
that the prior can be written as: p(X ) ∝ exp(−
1
2
||h
0
(X ) −
z
0
||
2
Ω
0
), for some given function h
0
(·), prior mean z
0
, and
information matrix Ω
0
. Since maximizing the posterior is
the same as minimizing the negative log-posterior, the MAP
estimate in (2) becomes:
X
?
= argmin
X
−log
p(X )
m
Y
k=1
p(z
k
|X
k
)
!
=
argmin
X
m
X
k=0
||h
k
(X
k
) − z
k
||
2
Ω
k
(4)
which is a nonlinear least squares problem, as in most prob-
lems of interest in robotics, h
k
(·) is a nonlinear function.
Note that the formulation (4) follows from the assumption of
Normally distributed noise. Other assumptions for the noise
distribution lead to different cost functions; for instance, if the
noise follows a Laplace distribution, the squared `
2
-norm in (4)
is replaced by the `
1
-norm. To increase resilience to outliers, it
is also common to substitute the squared `
2
-norm in (4) with
robust loss functions (e.g., Huber or Tukey loss) [112].
The computer vision expert may notice a resemblance
between problem (4) and bundle adjustment (BA) in Structure
from Motion [244]; both (4) and BA indeed stem from a
maximum a posteriori formulation. However, two key features
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