Chapter 2Movable MachinesDRAFT OF CHAPTER 2 (8 Jan 2013)(likely to be updated soon)Mobile Robotics: An Information Space ApproachSteven M. LaValle, University of IllinoisAll rights reserved.Mobile robots combine three kinds of systems:1. Actuation: Powered mechanical systems that cause motion.Examples are motors, thrusters, and propellers.2. Sensing: Devices that output signals in response to external stimuli.Examples are cameras, laser scanners, and microphones.3. Computation: One or more digital processors (CPUs) with memory.Examples are laptops, embedded processors, and microcontroller boards.Actuation is the topic of this chapter: If a signal is sent to the actuation system,what happens? The robot should move in some desired way. Ideally, it should movepredictably. In reality, it may move mostly as desired but with some unpredictableerrors. In either case, we want to characterize what will happen so that we canadd in the other two systems. Sensors will provide information that is used todecide whether to change the signals to the actuation system. Computation maybe needed to process the sensor readings and all prior information, and make adecision that helps solve the task. Sensors and computation are the subjects oflater chapters.2.1 Mechanical HardwareRobot locomotion is a general subject that addresses ways in which a mobile robotcould move. Locomotion is an old branch robotics, yet remains one of the most2526 S. M. LaValle: Mobile RoboticsFigure 2.1: A few legs that clumsily “roll” along can be considered as a rimlesswheel. Increasing the number of legs gradually produces a wheel.active areas of research. The particular choice of locomotion method depends onmany factors, such as:1. Medium: What kind of environment will the robot traverse? Examples arerugged terrain, factory floors, air, space, on top of water, and under water.2. Stability: Will the robot platform shake, vibrate, or tumble while moving?The robot might need to carry a camera that streams video without makingviewers sick. Alternatively, perhaps the robot carries delicate materials.3. Payload: How much weight will the robot be required to carry?4. Energy consumption: Mobile robots are notoriously limited by their bat-tery capacity. Low-energy methods of locomotion contribute greatly to theirlongevity.5. Durability: Can the robot survive extended use in harsh conditions such ascold weather, snow, rain? Can the robot overcome collisions with obstaclesand other robots?6. Cost: The lower the cost, the greater the likelihood that the robot will bemass produced, which leads to greater impact on society.Thousands of robot designs exist, which each address these factors in differentways. Chapter 1 showed robots that perform legged locomotion by walking throughindoor and outdoor environments. Refer to Figures 1.5(e) and 1.6. An importantdesign consideration is the gait, which specifies the motions of legs and the orderin which feet are placed on the ground and removed from the ground. Ensuringstability while one or more feet are not touching the ground is a challenging prob-lem. Other methods of locomotion that involve gaits include slithering snakes, theswimming robot of Figure 1.9(a), and the vibrating bug in Figure 1.13. Locomo-tion may also be achieved by thrusting, as in the case of the autonomous motorboat in Figure 1.9(b), the UAV in Figure 1.9(c), and the quad-rotor helicopter inFigure 1.10.2.1. MECHANICAL HARDWARE 27Figure 2.2: A low-cost robot built at the University of Illinois by extending theSERB open-source mobile design. The wheels and platform are cut from acrylicsheets. Each wheel is connected to a servo, and an Arduino microcontroller pro-vides commands.Finally, the oldest and most common form of locomotion was offered by theinvention of the wheel. By comparing to the rimless wheel shown in Figure 2.1,rolling locomotion is the beautiful limiting case of having an infinite number oflegs that continuously move in unison. This case will be the main focus for theremainder of this chapter; however, keep in mind that mathematical models ofother locomotion methods have similar forms. Most of the robots from Section 1.1move by rolling.For rolling locomotion, each wheel is usually connected to an axle that is turnedby a motor. A simple, low-cost design is shown in Figure 2.2. At the high end,virtually any car, truck, or construction vehicle that has been designed for humanuse has been retrofitted for automated driving. An example is the Google car fromFigure 1.5(c). Large robotic vehicles at the high end use sophisticated electricaland mechanical systems that incorporate sensor feedback and gearing to deliverpredictable, reliable performance. Most of these build on extensive automotivetechnology that has been developed over the past century. In addition, many un-usual rolling locomotion systems have been designed specifically for mobile robots.For example, the Mecanum (or Swedish) wheel (Figure 2.3) can roll both forwardas an ordin