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Classical control algorithms require an exact specification of reference values, however, it is difficult to give exact definitions of properties such as the warmth of a heater, the color of a piece of fabric or the speed of a car. Fuzzy logic uses rules on linguistic variables such as “fast” and “slow” to implement control algorithms. Values from the sensors are fuzzified into linguistic variables, then the rules are applied, and finally the consequents of the rules are defuzzified to obtain numerical values that can be applied to the actuators.

Cameras are essential in robots such as self-driving cars that are required to identify objects in the environment. Sensors in the camera return an array of pixels to which image processing algorithms are applied. The first step is to enhance the image to reduce noise and improve the contrast. The techniques used are spatial filters and histogram manipulation. The next step is to extract geometric properties in the image. Edges are identified using derivative filters, corners are identified by comparing pixels to their neighbors, and blobs are identified by comparing neighbors to a global threshold.

Robots are required to function in environments that are not known when the robot is programmed. The solution is to have the robot learn algorithms by itself. Artificial neural networks (ANN) are computerized models of neurons and their connections that over time can adapt themselves to perform a task. An ANN is defined by its topology: the number of neurons, the number of levels between the inputs and outputs, and the connections between neurons of adjacent levels. The second component of an ANN is an algorithm for learning. The Hebbian rule is an elementary form of reinforcement learning where the ANN receives feedback on which behaviors are good and which are not. The feedback is used to adjust the weights given to the input of each neuron in the ANN.

Machine learning (ML) algorithms perform classification. Given a large set of sensor data, an ML algorithm determines a discriminant that can classify future sensor data into the correct classes. Most ML algorithms are statistical. A simple form of ML uses the means and variances of the data from two sensors to choose the sensor that produces the better discriminant. An optimal discriminant can be obtained by combining data from two sensors using linear discriminant analysis (LDA). LDA depends on statistical properties of the samples that do not always hold. When LDA is not appropriate, perceptrons, which are related to neural networks, can be used to perform classification.

Distributed systems of multiple robots, called swarm robotics, are more robust than centralized systems consisting of single robots. The failure of one robot of a group need not prevent the others from performing a task. Furthermore, a group of collaborating robots can perform tasks that a single robot cannot. Swarm robotics is inspired by the behavior of colonies of insects such as ants and bees. Communications among the robots of a group can be direct, indirect (for example, by leaving markings) or physical. The BeeClust algorithm causes robots to cluster at areas of high sensor values by detecting collisions among them. The stick pulling algorithm demonstrates how two robots can collaborate to perform a task that neither could do alone. Occlusion-based pushing shows that a group of robots can collaborate even without explicit communications.

Robotic manipulators are widely used in industry. They are simpler than mobile robots in that they perform tasks in a fixed and known environment. They are more complex than mobile robots because they move in the three spatial dimensions and in the three dimensions of rotation. Using a simplified planar model of a robotic arm, the two central problems of manipulators are presented. Forward kinematics asks where the end effector of the arm will be following a sequence of rotations of the joints of the arm. Inverse kinematics asks what rotations of the joints will bring the end effector to a specified position. A rotation of a robotic manipulator is described by a rotation matrix whose elements are trigonometric functions of the angle of rotation. The rotation matrix for a planar rotation is derived followed by an overview of three-dimensional rotations.