ProbabilisticRobotics第二章總結(jié)

1、Key Topic 1: Robot Environment Interaction1 StateEnvironments are characterized by state.? State 滬? State at time t1) Typical State Variables? Robot pose: 6 state variables: (x, y, z) for Cartesian coordinates; (pitch, roll, yaw) for angular orientation (Kinematic State)? Configuration of the robot

2、s actuators? (Kinematic State)? Robot velocity and the velocities of its joints. 6 variables, each for 1 pose variabl?e (Dynamic State)? Location and features of surrounding objects in the environment.? Location and velocities of moving objects and people? A huge number of others?2) Complete State?

3、Best predictor of the future? Completeness entails that knowledge of past states, measurements or controls carry no additional information that would help us to predict the future more accurately?3) Incomplete State? In practice, it is impossible to specify a complete state for any realistic robot s

4、ystem? Therefore, practical implementations single out a small subset of all state variable?s T Incompleteness4) Hybrid State Space? State 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 acraeWcdHy

5、brid state spaces?2 Environment Interaction1) Two fundamental types of interaction between a robot and its environment:a) Robot T influence the state of T Environment (Via actuator)? Control actions.? Always execute a control action, even when no motor is move?db) Robot & gather state info from

6、A-Environment (Via sensor)? Percept, observation or measurement. ? Always have delays?2) Two different data streams:a) Measurement data?b) Control data：U/3 Probabilistic Generative LawsThe probabilistic law characterizing the evolution of state: depending on all past states, measurements and contr?o

7、lsIf state x is complete,?嗆屁一血"叫)=PgTransition.P(zt I xo: t>-卩 I A 八Measurement Probability4 Belief DistributionsA belief reflects the robots intenial knowledge about the state of the environmen?t A belief, or state of knowledgewith regards to a state should be distinguished from the true st

8、ate itself. We,which is an abbreviation for the posteriordenotebbedl(iexft) = p(xjz 1:f/u1：r)assumed that belief is taken after incorporating the measurement "We denote posterior before incorporating as follows:=ul：t)which is also referred to asprediction in the context of probabilistic filteri

9、ng. Calculating 力口心 from 叫丿 js called correction or the measurement update.Ke)y Topic 2:Bayes FiltersThe Bayes Filter Algorithm1:2:3:4：5:ao:atAlgorithm Bayes_filter 嚴(yán)'厲一for all do況 7(可)=Jp(xr| uvxt_x)bel(xt_x)dx belAx) = rp(z tx()Aelxt)en dfort belxt)return '"The algorithm has two essential steps First step is called control updatepr bel(x" predicti on. The sec ond step is called the measureme nt updateTo compute the posterior belief recursively, the algorithm requires an ini