Probabilistic Robotics

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## Probabilistic Robotics

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**Probabilistic Robotics**Introduction**Robotics is the science of perceiving and manipulating the**physical world through computer-controlled devices. • Desirability of “intelligent” manipulating devices. Examples… • To be intelligent, robots have to accommodate the enormous uncertainty that exists in the physical world. Introduction**Where does Uncertainty come from?**• robot environmentsare inherently unpredictable. Assembly line, high way, private homes (highly dynamic and highly unpredictable) • Sensors range and resolution,noise… • Robot actuation motor, control noise,wear-and-tear, mechanical failure…. • robot software, internal models of robots are crude and approximate. Model errors are a source of uncertainty that has often been ignored in robotics, despite the fact that most robotic models used in state-of-the-art robotics systems are rather crude. • Algorithmic approximation Introduction**As robotics is now moving into the open world, the issue of**uncertainty has become a major stumbling block for the design of capable robot systems. • Managing uncertainty is possibly the most important step towards robust real-world robot systems. • Hence Probabilistic Robotics Introduction**Introduction- Probabilistic Robotics**• A relatively new approch robotics. • The key idea is to represent uncertainty explicitly using the calculus of probability theory. • Maintaining a probability distribution instead of a single best guess. • It outperforms alternative techniques in many real-world applications.**Examples using Probabilistic Robotics.**• Mobile Robot Localization • The problem of estimating a robot‘s coordinates relative to an external reference frame. Map of environment is given, find out where I (the robot) am. Can consulte sensor data and can move around. • See Figure 1.1 Introduction- Probabilistic Robotics**Introduction- Probabilistic Robotics**Examples using Probabilistic Robotics. • Robotic Planning and Control • Coastal navigation • See Figure 1.2**Implication of Probabilistic Robotics**• Probabilistic robotics seamlessly integrates models with sensor data, overcoming the limitations of both at the same time. • A bit of history of robotics research • Model-based paradigm • Behavior-based paradigm • Probabilistic robotics tends to be more robust in the face of sensor limitations and model limitations. Scale much better to complex real-world environments. • Probabilistc approachs are currently the only known working solutions to hard robotic estimation problems, such as localization and mapping**Implication of Probabilistic Robotics**• Probabilistic robotics have weaker requirements on the accuracy of the robot‘s models, and weaker requirements on the accuracy of robotic sensors, compared with previous approaches. • Probabilistic robotics is also criticized because of • Computational complexity, and • Need to approxiamte.**Probabilistic Robotics**Recursive State Estimation**Recursive State Estimation**• Give me the sensor data, I will tell you something. • Estimate state from sensor data. • This is the core idea of probabilistic robotics. • Probabilistic state estimation algorithms comopute belief distributions over possible world states. An example, already shown, what is it? • The purpose of this part of lecture • Introduce notions and notions that will be used. • Background preparation • Introduce the algiorthm Bayes filters, the single most important algorithm that is the basis of virtually every techniques presented in the book.**Axioms of Probability Theory**Pr(A) denotes probability that proposition A is true.**B**A Closer Look at Axiom 3**Discrete Random Variables**• Xdenotes a random variable. • Xcan take on a countable number of values in {x1, x2, …, xn}. • P(X=xi), or P(xi), is the probability that the random variable X takes on value xi. • P( ) is called probability mass function. • E.g.**Continuous Random Variables**• Xtakes on values in the continuum. • p(X=x), or p(x), is a probability density function. • E.g. p(x) x**Joint and Conditional Probability**• P(X=x and Y=y) = P(x,y) • If X and Y are independent then P(x,y) = P(x) P(y) • P(x | y) is the probability of x given y P(x | y) = P(x,y) / P(y) P(x,y) = P(x | y) P(y) • If X and Y are independent thenP(x | y) = P(x)**Law of Total Probability, Marginals**Discrete case Continuous case**Normalization**Algorithm:**Conditioning**• Law of total probability:**Conditional Independence**equivalent to and**Robot Environment Interaction**• See Figure 2.1 • The robot maintains an internal belief with regards to the state of its environment. • The robot also influence its environment through its actuators. • Uncertainty exists, as always….**Robot Environment Interaction**• Environment are characterized by state variables. • State can be conveniently considered as the collection of all aspects of the robot and its environment that can impact the future. • Dynamic state variable and static state variable? • State is denoted , the state at time t is denoted**Robot Environment Interaction**• Typical state variables: • Robot pose, • Configuration of the robot’s actuators, • Robot velocity, • Location and features of surrounding objects in the environment • Landmarks are distinct, stationary features of the environment that can be recognized reliably. • Location and velocities of moving objects and people… • Whether sensor is broken. • The list can go on and on…..**Robot Environment Interaction**• Complete State • Markov Chains • You want to know if tomorrow is going to rain, you only need to know….. • Incomplete State • A complete state is hard to obtain, we get by with a small subset of complete state. • In most robotics applications, the state is continuous, meaning that is defined over a continuum. For example… • Sometimes, the state can be discrete. • Thus hybrid state space….**Robot Environment Interaction**• Two fundamental types of interactions between a robot and its environment. • 1. The robot can influence the state of its environment through its actuators. • The control actions • 2. The robot can gather information about the state through its sensors. • The environment sensor measurements • How to probabilistically model these interactions?