Probabilistic Robotics 第二章总结

key topic 13360 robot environment interaction1状态环境are characterized by state。状态xState at time t XT1) Typical State Variablesrobot pose : 6 state variables :(x、y、z)for cartesian coordinates；(pitch，roll，yaw)for angular orientation(kinematic state)configuration of the robots actuators。(kinematic state)robot velocity and the velocities of its joints . 6 variables，each for 1 pose variable。(动态状态)location and features of surrounding objects in the environment。location and veloces of moving objects and people。休眠号of others。2)完全状态Best predictor of the future。completed ness entails that knowledge of past States，measurements or controls carry no additional information that would help us to predict that3) Incomplete StateIn practice，it is impossible to specify a complete state for any realistic robot system。Therefore，practical implementations single out a small subset of all state variables . in completed ness4) Hybrid State SpaceState can be continuous (e.g .robot pose)，can be discrete (e.g .sensor broken or not)。state spaces that contain both continuous and discrete variables are called hybrid state spaces。2 Environment Interaction1)two fundamental types of interaction between a robot and its environment :a)robot influence the state of environment(via actuator)控件行为。Always execute a control action，even when no motor is moved。b)robot gather state info from environment(via sensor)Percept，observation or measurement。Always have delays。2) Two different data streams:A) Measurement data:ztb)控制data:ut3 Probabilistic Generative Lawsthe probability law character izing the evolution of state :P (XT | x0: t-1，z 1: t-1，u 13360t)Depending on all past States，measurements and controls。If state x is complete、P (XT | x0: t-1，z 13360t-1，u 13360t)=pxt XT-1，ut)状态转移Pztx033369t，z 1: t-1，u 1:t=pzxtmeasurement probability4 Belief Distributionsa belief reflects the robot s internal knowledge about the state of the environment .a belief，or state of knowledge with regards to a state should be distinguished from the true state itself .we denote belief over a state variable XT by bel(XT)，which is an abbreviation for the posteriorBelxt=p(xt|z1:t，u1:t)assumed that belief is taken after incorporating the measurement ZT。we denote posterior before incoorporating ZT as follows :Belxt=pxtz1:t-1，u1:t)which is also referred to as prediction in the context of probability filtering。calculating bel(XT)from be lxt is called correction or the measurement update。Key Topic 2:Bayes FiltersThe Bayes Filter Algorithm1: algorithm Bayes _ filter(be lxt-1，ut，ZT) :2:for all XT do3: be lxt=pxtut，XT-1be lxt-1dx43360 be lxt=pzxtbelxt5:endfor6:return belxtthe algorithm has two essential steps . first step is called control update，or prediction . the second step is called the measurement update。to compute the posterior belief recursively，the algorithm requires an initial be