Classi fi cation of Robots
Industrial Robots
The factory assembly line can operate without the presence of humans in a well-defined environment where the robot must perform tasks in a specified sequence, acting on objects that are precisely positioned in front of it (Fig.1.3). However, their design is simplified because they work in a customized environment that humans do not have access to while the robot is working.
Autonomous Mobile Robots
These are extremely difficult to develop due to the highly complex uncertain environment of motorized traffic and strict safety requirements. Better sensors can perceive the details of more complex situations, but to handle these situations, the robot's behavior control must be very flexible and adaptable.
Humanoid Robots
Much of the research and development in robotics today is focused on making robots more autonomous by improving sensors and enabling more intelligent control of the robot. This involves both sensing and intelligence, but it must also take into account the psychology and sociology of the interactions.
Educational Robots
End effectors can be built with robotics kits or by using additional components with pre-assembled robots, although educational robotic arms exist (Fig.1.6b). It uses event-action pairs: when the event represented by the block on the left occurs, the actions in the following blocks are executed.
The Generic Robot
- Differential Drive
- Proximity Sensors
- Ground Sensors
- Embedded Computer
A horizontal proximity sensor can measure the distance (in centimeters) from the robot to an object and the angle (in degrees) between the front of the robot and the object. The figure shows the robot from above, although the ground sensors are at the bottom of the robot.
The Algorithmic Formalism
They are also used for polling, an alternative to event handlers: instead of performing a calculation when an event occurs, sensors are read and stored periodically. More specifically, polling occurs as an event handler when a timer expires, but software design using polling can be quite different from event-based software design.
An Overview of the Content of the Book
This chapter introduces fuzzy logic and shows how it can be used to control a robot approaching an object. This chapter presents an approach to learning: artificial neural networks modeled on neurons in our brains.
Summary
This chapter presents a simplified treatment of the fundamental concepts of robot manipulators (forward and reverse kinematics, rotations, homogeneous transformations) in two dimensions, as well as a taste of three-dimensional rotations. Appendix B Mathematical Derivations and Tutorials This chapter contains tutorials that discuss some of the mathematical concepts used in the book.
Further Reading
When an object is detected to the right of the robot, the robot turns right. When an object is detected to the left of the robot, the robot turns left.
Classi fi cation of Sensors
Distance Sensors
- Ultrasound Distance Sensors
- Infrared Proximity Sensors
- Optical Distance Sensors
- Triangulating Sensors
- Laser Scanners
Light intensity decreases with the square of the distance from the source, and this ratio can be used to measure the approximate distance to the object. Secondly, a laser beam is highly focused so that an accurate measurement of the angle to the object can be made (Fig.2.3).
Cameras
Given the position of the camera, what part of the sphere surrounding the camera is captured in the image. Cameras with a wide field of view are used in mobile robots because the image can be analyzed to understand the environment.
Other Sensors
An important feature in designing a camera for a robot is the field of view of its lens. The analysis of the image is used for navigation, to locate objects in the environment and to communicate with humans or other robots using visual properties such as color.
Range, Resolution, Precision, Accuracy
If a distance sensor consistently claims that the distance is 5 cm greater than it actually is, the sensor is not accurate. Place an object at different distances from the robot and measure the distances returned by the sensor.
Nonlinearity
Linear Sensors
Stick a ruler on your table and carefully place the robot so that its front sensor is placed next to the 0 mark of the ruler.
Mapping Nonlinear Sensors
If you look again at the graph in Fig.2.13, you can see that the segments of the curve are roughly linear, although their slopes change according to the curve. Therefore, we can get a good approximation of the distance corresponding to a sensor reading by taking the relative distance on a straight line between two points (Fig.2.14).
Summary
One solution is to take the closest value, so if the value 27 is returned by the sensor whose mapping is given in Table 2.1, the distance would be 12.
Further Reading
Purely reactive behavior occurs when the action is only related to the occurrence of an event and does not depend on data stored in memory (state). Sections 3.1–3.3 describe Braitenberg vehicles exhibiting reactive behavior; in Chapter 4 we present Braitenberg vehicles that do not respond to states.
Braitenberg Vehicles
Calibration is necessary to determine the optimal thresholds for fast robust movement of the robot. 40 3 Reactive behavior was the precursor to the LEGO®Mindstorms robotics kits.1 This chapter describes an implementation of most of the Braitenberg vehicles from the MIT report.
Reacting to the Detection of an Object
Specification (Dogged (stop)): As in activity 3.3, but when an object is not detected, the robot stops. Specification (Attractive and Repulsive): When an object approaches the robot from behind, the robot runs away until it is out of range.
Reacting and Turning
Specification (Paranoid (Right-Left)): When an object is detected in front of the robot, the robot moves forward. If an object is detected to the left of the robot, turn off the right motor and set the left motor to rotate forward.
Line Following
Line Following with a Pair of Ground Sensors
46 3 Reactive Behavior For now, we specify that the robot will stop when neither sensor detects the line. If the turn is too sharp, the robot on the other side of the line may run away.
Line Following with only One Ground Sensor
Hint: The only problem is when the robot crashes from the black side of the line, because there the algorithm does not distinguish between this case and the white side of the line. One solution is to use a variable to remember the previous value of the sensor so that the two cases can be distinguished.
Line Following Without a Gradient
Since the sensor values are proportional to the gray scale of the line, the approximate distance of the sensor from the center of the line can be calculated. Compare the performance of the algorithm with the linear following algorithms using two sensors and one sensor with a gradient.
Braitenberg ’ s Presentation of the Vehicles
The robots in Fig.3.8a–b are the same as the robots in Fig.3.7a–b, respectively, except that the sensor values are negated (signs on the connections): the more light detected, the slower the wheel will turn. Suppose there is a fixed bias applied to the motors so that the wheels turn forward when no light source is detected.
Summary
Use proximity sensors instead of Braitenberg's light sensors and the detection or non-detection of an object instead of stronger or weaker light sources.
Further Reading
The images or other third-party materials in this chapter are included under the Creative Commons license of the chapter, unless otherwise noted in a line of credit accompanying the materials. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by law or exceeds the permitted use, you must obtain permission directly from the copyright holder.
State Machines
Braitenberg vehicles and line-following algorithms (Chap.3) demonstrate reactive behavior, where the robot's action depends on the current values returned by the robot's sensors, not on events that have occurred before. The action is not continuing; for example, the action rotate left means to set the motors so that the robot turns left, but the transition to the next state is done without waiting for the robot to reach a specific position.
Reactive Behavior with State
Search and Approach
The object has been detected but the search is not at an edge of the sector; in this case, the pass is taken. The search is at one end of the sector, but an object has not been detected; in this case, left-to-right or right-to-left transition is taken.
Implementation of Finite State Machines
The search is at an edge of the sector exactly when an object is detected; in this case an arbitrary transition is taken. That is, the robot can approach the object or it can change the direction of the search.
Summary
Further Reading
Real-world robots must move to specific locations and may have engineering limitations on how fast or slow they can move or turn. In the simplest implementation, the speed of the robot's wheels is assumed to be proportional to the power used by the motors.
Distance, Velocity and Time
Use a stopwatch to measure the time it takes for the robot to move between the lines. To accurately navigate an environment, a robot must detect objects in its environment, such as walls, floor markings, and objects.
Acceleration as Change in Velocity
When the robot's power setting is set to a fixed value, the force on the robot is constant and we expect the acceleration to remain constant, increasing the speed. But at a certain point, the acceleration is reduced to zero, which means that the speed no longer increases, because the force on the wheels is just sufficient to overcome the friction of the road and the wind resistance.
From Segments to Continuous Motion
When the robot appears to have reached full speed, record the time since the start of the run. Calculate velocities from distances divided by time and compare tov=at (Figure 5.2a).
Navigation by Odometry
Linear Odometry
Once the relationship between motor power and speeds is determined, the robot can calculate the distance traveled s=vt. If the robot starts at the origin (0,0) and moves in a straight line at an angle θ with speed v for time, the distance moved is iss=vt.
Odometry with Turns
If the distance is small, the line labeled dcis is approximately perpendicular to the radius through the robot's final position. With similar triangles, we see that θ is the change in the robot's course (Fig.5.5).
Errors in Odometry
Write a program that causes the robot to move in a straight line 2 m and then turn 360◦. Write a program that causes the robot to turn 360◦ and then move in a straight line 2 m.
Wheel Encoders
Watch the video and determine the number of revolutions by counting the number of times the mark is at the top of the wheel. Determine the number of revolutions by counting the number of times a mark is at the top of the wheel and dividing by.
Inertial Navigation Systems
Accelerometers
The direction in which the mass moves indicates the acceleration: forward or backward. The magnitude of the force is measured indirectly by measuring the distance the mass moves.
Gyroscopes
Two square masses are attached by flexible beams to anchors mounted on the base of the component. The Coriolis force is a force whose direction is given by the vector cross product of the axis of rotation and the motion of the mass, and whose magnitude is proportional to the linear velocity of the mass and the angular velocity of the gyro.
Applications
The masses (grey squares) are forced to vibrate at the same frequency as the two legs of a tuning fork. Since the masses move in different directions, the resulting forces will be equal but in opposite directions (solid arrows).
Degrees of Freedom and Numbers of Actuators
A differentially driven robot has two actuators, one for each wheel, even though the robot itself has three DOF. The two-jointed arm in Fig. 5.11 has two motors, one at each rotating joint, so the number of actuators is equal to the number of DOF.
The Relative Number of Actuators and DOF
The mobile arm robot (Fig.5.13b) has three actuators: a motor that moves the robot forward and backward, and motors for each of the two rotary joints. For the mobile arm robot (Fig.5.13b), there are an infinite number of base and arm positions that bring the end effector to a specific reachable position.
Holonomic and Non-holonomic Motion
To directly access the third OF, the robot must be able to move laterally. Two pairs of wheels on opposite sides of the robot can directly move the robot left, right, forward and backward.
Summary
Further Reading
For example, if a robot is to bring an object from a shelf in a warehouse to a delivery track, it must use sensors to navigate to the correct shelf, detect and grab the object, and then navigate back to the truck and load the object. In a warehouse there may be obstacles on the way to the shelf, the object will not be placed exactly on the shelf and the truck is never parked in the same place.
Control Models
Open Loop Control
Closed Loop Control
For example, if the reference value is the position of the robot relative to the shelf, the control value will be the power setting of the motors and the duration of operation of the motors. The variable kay represents the result, that is the actual state of the robot, for example the distance to the object.
The Period of a Control Algorithm
A 1 ms control period would waste computational power because the robot will only move 0.002 cm (0.02 mm) during each 1 ms cycle of the control algorithm. In the example, we concluded that the optimal period of the control algorithm was in the order of tenths of a second.
On-Off Control
The resulting behavior of the robot is shown in Fig.6.2: the robot will oscillate around the reference distance to the object. It is highly unlikely that the robot will actually stop at or near the reference distance.
Proportional (P) Controller
In theory, the low power setting should cause the robot to move slowly and eventually reach the reference distance. The P-controller sets the maximum motor power to make the robot move quickly towards the object.
Proportional-Integral (PI) Controller
Apply the proportional control algorithm to make the robot stop at a certain distance from an object. Implement a PI controller that causes the robot to stop at a certain distance from an object.
Proportional-Integral-Derivative (PID) Controller
Compare the behavior of the PI controller with a P controller for the same task by monitoring the variables of the control algorithms over time. What happens if you manually prevent the robot from moving for a short time and then let it go.
Summary
Further Reading
Self-driving car navigation can be divided into two tasks: There is a high-level task of finding the path between the starting position and the destination position. While high-level pathfinding can be done once before a trip (or every few minutes), the low-level task of obstacle avoidance must be done frequently, since the car never knows when a pedestrian will jump into the road or when a car following it will suddenly brake.
Obstacle Avoidance
Wall Following
The robot will never detect the target, so it will move indefinitely around the first obstacle.
Wall Following with Direction
After four left turns, its bearing is 360◦ (also north, a multiple of 360◦ ) and it continues to move forward, repeatedly encountering and following the wall. Implement the directional wall tracking algorithm and verify that it exhibits the behavior shown in Figure 7.4.
The Pledge Algorithm
Following a Line with a Code
We do not need a federated localization algorithm like those in Chapter 8, we only need to know the positions on the line that facilitate the task. Navigation without continuous localization can be done by reading a code placed on the floor next to the bar.
Ants Searching for a Food Source
The food source is represented by a dark spot that can be easily detected by a ground sensor on the robot. The robot's proximity sensors are used to detect the walls of the area.
A Probabilistic Model of the Ants ’ Behavior
Figure 7.11 shows the probability of an ant's location after finding a food source, returning to the nest, and making another random move. Although ants move randomly, their behavior of returning to the nest after finding a food source makes them more likely to be on the diagonal than anywhere else in the environment.
A Finite State Machine for the Path Finding Algorithm
Therefore, the robot (or its sensor) has to turn until it finds the direction to the nest. When it does, it turns to the nest and takes the transition to the stategoto nest.
Summary
Since the nest is next to a wall, this condition is also true when the robot returns to the nest. We specified that the nest can be detected (Activity 7.7), but the robot's sensor is not necessarily facing the direction of the nest.
Further Reading
If the robot sees a high-density (black) marker, it concludes that it has reached the food source and transitions to the state of food. This state is similar to the following state in that the robot moves forward toward the nest and turns right or left as needed to move toward the nest.
Landmarks
For a robot, what does it mean to "count steps" and "open our eyes every now and then". Now and then you can open your eyes for a second; this action costs 1 point.
Determining Position from Objects Whose Position
Determining Position from an Angle
From the known absolute coordinates of the object (x0,y0), the coordinates of the robot can be determined. The distance and the angle are measured from the position where the sensor is mounted, which is not necessarily the center of the robot.
Determining Position by Triangulation
To measure azimuth, line up the robot with one edge of the table and call it north. First, perform an angle measurement at one position and then pick up the robot and move it to a new position for the second measurement, carefully measuring the distance.
Global Positioning System
Probabilistic Localization
Sensing Increases Certainty
As time goes on, the uncertainty decreases: the robot knows with greater certainty where it is actually located. In this example, the robot finally knows its position by 6 with full certainty or it has reduced its uncertainty to one of the two positions 2,7.
Uncertainty in Sensing
For example, the 0.19 probability that the robot was in position 1 now becomes the probability that it is in position 2. Similarly, the 0.02 probability that the robot was in position 3 now becomes the probability that it is in position 4.
Uncertainty in Motion
138 8 Localization Table 8.2 Localization with uncertainty in sensitivity and movement, sensor=after multiplying by the uncertainty of the sensor, norm=after normalization, right=after moving right one position. The robot is likely in position 6, but we are less sure because the probability is only 0.43 instead of 0.63.
Summary
Further Reading
Maps are less relevant for a robot vacuum cleaner, because the manufacturer cannot prepare maps of the apartments of each customer. Observations of the sun and stars were used for localization and maps were created as exploration continued.
Discrete and Continuous Maps
In Fig.9.1b, three pairs of numbers represent the triangle with much greater accuracy than the seven pairs of the discrete map. Furthermore, it is easy to calculate whether a point is in the object or not by using analytic geometry.
The Content of the Cells of a Grid Map
Place your robot on a line in front of a series of obstacles that the robot can detect with a side sensor (Figure 9.3). Otherwise, draw regular lines on the ground that the robot can read for localization.
Creating a Map by Exploration: The Frontier Algorithm
Grid Maps with Occupancy Probabilities
The red lines of small squares in Fig.9.4 represent the boundary between the border and the unknown cells in the environment. The unknown cells adjacent to the border are the interesting ones that need to be explored to expand the current map.
The Frontier Algorithm
The example to which we applied the frontier algorithm is a relatively simple environment consisting of two rooms connected by a door (in the sixth column from the left in Figure 9-9), but otherwise isolated from the outside environment. Each robot will explore that part of the boundary closest to its position.
Priority in the Frontier Algorithm
Since each robot explores a different area of the environment, the construction of the map will be much more efficient. You will need to include an algorithm to accurately move from one cell to another and an algorithm to move around obstacles.
Mapping Using Knowledge of the Environment
Measuring over a large area enables the robot to identify features such as walls and corners from a measurement taken at a single location. How large must the landmarks be for the robot to reliably detect them.
A Numerical Example for a SLAM Algorithm
The actual position of the robot is shown in Fig.9.17a and b is the corresponding map. However, due to the odometry error, the actual perception of the robot is different.
Activities for Demonstrating the SLAM Algorithm
From a series of measured observations, calculate their correspondences to the observations of the robot's 15 postures. Calculate the perception (d, θ) of the object from this attitude and then calculate the coordinate (x, y) of the new obstacle.
The Formalization of the SLAM Algorithm
Summary
Further Reading
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, modification, distribution, and reproduction in any media or format, so long as you properly credit the original author(s) and source, provide a link to the Creative Commons license, and indicate if changes have been made. Think of a robot used in a hospital to transport medicines and other supplies from storage areas to the doctors and nurses.
Dijkstra ’ s Algorithm for a Grid Map
Dijkstra ’ s Algorithm on a Grid Map with Constant
Figure 10.3a shows the network map after five iterations and Fig.10.3b shows the final network map after nine iterations when the goal cell is reached. The upper left diagram shows the network map after three iterations and the upper right diagram shows the map after 19 iterations.
Dijkstra ’ s Algorithm with Variable Costs
Finally, in the lower left diagram, G is found after 25 iterations, and the shortest path is indicated in gray in the lower right diagram. The right diagram shows the shortest path if the cost of moving through a cell of sand is only 2.
Dijkstra ’ s Algorithm for a Continuous Map
Place some obstacles in the grid and enter them on the robot's map. In this case, the shortest path in terms of the number of edges is also the geometrically shortest path.
Path Planning with the A Algorithm
The rest of the figure shows four stages of the algorithm leading to the shortest path to the target. Comparing Figures 10.4 and 10.12, we see that the A∗ algorithm only had to visit 71% of the cells visited by Dijkstra's algorithm.
Path Following and Obstacle Avoidance
Modify your implementation of the line-following algorithm so that the robot behaves correctly even if an obstacle is placed on the line. Modify your implementation of the line-following algorithm so that the robot behaves correctly even if additional robots move randomly in the region of the line.
Summary
Further Reading
Fuzzify The values of the sensors are converted to values of the linguistic variables, such as asfar, closing, near, calledpremises. Defuzzify The consequences are combined to produce acrispoutput, which is a numerical value that controls some aspect of the robot, such as the power supplied to the motors.
Fuzzify
If the value of the sensor is below far_low, then we are absolutely certain that the object is far and the certainty is 1. If the value is between close_low and far_height then we are somewhat certain that the object is far, but also somewhat certain that it is closing.
Apply Rules
The x-axis is the value returned by the sensor, and their axis gives the premise for each variable, the certainty that the language variable is true. For the value v, the certainty of the consequence is much smaller than the certainty obtained from the minimum function.
Defuzzify
Figure 11.3 shows the trapezoids for the resulting cruise with certainty 0.4 and the resulting fast with certainty 0.2. The value is closer to the value associated with cruising than the value associated with fast.
Summary
Set the appropriate thresholds for the proximity sensor and the appropriate defuzzification values to get the clean motor speed. The disadvantage is that the control behavior with fuzzy logic is not as transparent as with classical control algorithms.
Further Reading
In this chapter, we present a flavor of algorithms for digital image processing and describe how they are used in robotic systems. Sections 12.3–12.6 describe image processing algorithms: digital filter enhancement and histogram manipulation, segmentation (edge detection), and feature recognition (corner and blob detection, multiple feature identification).
Obtaining Images
This results in a one-dimensional array of pixels that can be processed by simplified versions of the algorithms we present. The sensors can measure light of wavelengths outside the range we call visible light: longer-wavelength infrared light and shorter-wavelength ultraviolet light.
An Overview of Digital Image Processing
Infrared imaging is important in robotics because hot objects such as people and cars can be detected as bright infrared light. Section 12.6 describes how to identify blobs, which are areas whose pixels have similar intensity but are not bounded by regular features such as lines and curves.
Image Enhancement
Spatial Filters
A program can make each pixel more like its neighbors by replacing the pixel's intensity with the average of its intensity and the intensity of its neighbors. 3 The filter is not applied to pixels at the border of the image to avoid exceeding the group boundaries.
Histogram Manipulation
Program the robot to move from left to right across the pattern, sampling the ground sensor output. Modify the program so that it replaces each sample with the average of the intensity of the sample and its two neighbors.
Edge Detection
Examine the histogram to determine a threshold value that will be used to distinguish between the black lines and the background. Calculate the sum of the contents of the containers until the sum is greater than a fraction (perhaps a third) of the samples.
Corner Detection
Recognizing Blobs
Summary
Further Reading
The Biological Neural System
The Arti fi cial Neural Network Model
Implementing a Braintenberg Vehicle with an ANN
Arti fi cial Neural Networks: Topologies
Multilayer Topology
Memory
Spatial Filter
Learning
Categories of Learning Algorithms
The Hebbian Rule for Learning in ANNs
Summary
Further Reading
Distinguishing Between Two Colors
A Discriminant Based on the Means
A Discriminant Based on the Means and Variances
Algorithm for Learning to Distinguish Colors
Linear Discriminant Analysis
Motivation
The Linear Discriminant
Choosing a Point for the Linear Discriminant
Choosing a Slope for the Linear Discriminant
Computation of a Linear Discriminant
Comparing the Quality of the Discriminants
Activities for LDA
Generalization of the Linear Discriminant
Perceptrons
Detecting a Slope
Classi fi cation with Perceptrons
Learning by a Perceptron
Numerical Example
Tuning the Parameters of the Perceptron
Summary
Further Reading
Approaches to Implementing Robot Collaboration
Coordination by Local Exchange of Information
Direct Communications
Indirect Communications
The BeeClust Algorithm
The ASSISIbf Implementation of BeeClust
Swarm Robotics Based on Physical Interactions
Collaborating on a Physical Task
Combining the Forces of Multiple Robots
Occlusion-Based Collective Pushing
Summary
Further Reading
Forward Kinematics
Inverse Kinematics
Rotations
Rotating a Vector
Rotating a Coordinate Frame
Transforming a Vector from One Coordinate Frame
Rotating and Translating a Coordinate Frame
A Taste of Three-Dimensional Rotations
Rotations Around the Three Axes
The Right-Hand Rule
Matrices for Three-Dimensional Rotations
Multiple Rotations
Euler Angles
The Number of Distinct Euler Angle Rotations
Advanced Topics in Three-Dimensional Transforms
Summary
Further Reading
