Abstract
Mathematics allows us to study robots so we can engineer them. Robots model aspects of motion, forces acting on/within the robot, its surroundings, and uncertainty when making decisions using mathematics. If you can understand a mathematical model of a robot, you can reason about how the robot will behave. Robotics uses mathematics tools from areas such as kinematics (the mathematics of motion without regard to forces or torques that cause motion), dynamics (adds forces/torques to kinematics), and feedback control (allows the robot to change its output to reach a desired behaviour). One example of feedback control is the PID (Proportional–Integral–Derivative) controller. These topics all come into play when a robot moves through its environment, grabs objects, and so on. They are also used when simply controlling the speed of a robot. In a robotics course, students learn mathematics topics such as algebra, trigonometry, linear algebra, and introductory calculus. They use these to learn about topics like coordinate transforms, trajectory generation, robot modelling, and sensor modelling. This allows students to reason about how to solve complicated problems. After learning how to reason mathematically about robots, students can begin to understand how a robot operates and make decisions. This is the first step to creating more autonomous systems.