Driverless vehicles have the potential to no only change the way we commute but the way we go about our daily lives. All journeys start with a single step. The first step in this activity it determining the best equation for a driverless vehicle to use to safely exit a parking space. Students use trigonometric functions, polynomials and piecewise functions to build the optimum curve, then test it for real using a TI-Rover.
- Transformations of a trigonometric function
- Transformations of a polynomial function
- Derivative of a polynomial
- Anti-derivative of a polynomial
- Simultaneous equations
- Distance between a point and function
- Define and build a hybrid (piecewise) function
- Point of inflexion
- Hybrid or Piecewise
- Join smoothly = equal gradients
About the Lesson
Students use trigonometric, polynomial and hybrid (piecewise) functions to generate a path for the TI-Innovator Rover to follow with a view to safely exiting a parking space. Simulations are available via interactive content in the TI-Nspire file before road testing with Rover. Students use calculus to ensure that the start and finish of Rover's path finish parallel to the curb and in the case of the hybrid functions, that the curves join smoothly. In addition to a wealth of mathematics, students gain an insight to the amount of mathematics required by driverless vehicles so that they may navigate successfully.