Simultaneous Localization and Mapping (SLAM)讲义1
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转自:http://blog.csdn.net/akunainiannian/article/details/45344055 (转载未经同意,请见谅)
简介:Slam问题的核心是将一个移动机器人放置在一个未知环境中,机器人通过自身传感器逐步建立环境的地图同时使用这张地图计算自身的位置。Slam问题由R. Smith, M. Self, and P.Cheeseman在1990年的一篇论文中提出。这个问题被认为是机器人领域的“圣杯”。因为它将使得机器人可以在毫无先验知识的环境中进行动作。
Slam问题由明显的结构,它有两个问题组成,一个是定位问题(localization),另一个是构建地图问题(Mapping)。
Localization problem:已知一张地图中有若干路标landmark,对这些路标进行测量,获得了他们的测量位置zk,然后通过zk再决定机器人的位置xk。在获取路标位置的过程中如有噪声,需要滤波。
Mapping problem:机器人的位置Xk已经知道,对路标点进行测量,获得测量位置zk,给予zk创建map m。
Slam 问题的基础:
过程模型(process model):一个已知动力学模型的机器人通过拥有若干路标landmark的环境。
观测模型(observation model):机器人装备了若干传感器,他们可以测量任意路标间的相对位置,以及机器人自身的位置。
其中过程模型:
方便初步理解,我们采用线性模型。把机器人的位置状态命名为:xv(k),模型为:
– Fv(k) is the state transition matrix
– uv(k) is a vector of control inputs
– wv(k) is a vector of uncorrelated process noise errors with zero mean and covariance Qv(k)。
对于第i个路标的状态传递方程是:
Slam问题认为路标是不动的。
那么,机器人位置了路标位置的联合状态变量可以表示为:
系统的状态方程是:
– Ipi is the dim(pi) x dim(pi) identity matrix
– 0pi is the dim(pi) null vector
观测模型(observation Model):
对于第i个路标的观测模型是:
– vi(k) is a vector of uncorrelated observation errors with zero mean and
variance Ri(k)
– Hi is the observation matrix that relates the sensor output zi(k) to the state vector x(k) when observing the ith landmark and is written as
离散的状态xk需要从对环境的测量zk中估计得出。这正是kalman filter的用武之地。
参考文献:
1、Dissanayake, M. W. M. G., et al. "A solution to the simultaneous localization and map building (SLAM) problem." Robotics and Automation, IEEE Transactions on 17.3 (2001): 229-241.
2、Durrant-Whyte, Hugh, and Tim Bailey. "Simultaneous localization and mapping: part I." Robotics & Automation Magazine, IEEE 13.2 (2006): 99-110.
3、Bailey, Tim, and Hugh Durrant-Whyte. "Simultaneous localization and mapping (SLAM): Part II." IEEE Robotics & Automation Magazine 13.3 (2006): 108-117.
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- Simultaneous Localization and Mapping (SLAM)讲义1
- Simultaneous Localization and Mapping (SLAM)讲义1
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