Problem:

What is a raceline? Parametrize a raceline? Evaluation cateria of raceline? Optimize?

Splines and Trajectories

Paramterize the path as a spline:

• The shape of path changed by changing the parameters of the spline
• Easier to sample the points on the spline to define the path as (x,y) coordiantion

A spline is a piecewise polynomial.

How are all segments fit togehter nicely?

Co Continiuity: continuous in position

Co and Ci Contrinuity: continuous in position and tangent line

Co, C1, C2 Continiity: continious in position, tangent line, and curvature

Cubic Splines: cubic piecewise polynomails are the most common. Allow gradient to be defined at each point

Gives local control. higher and lower degrees possible.

Setting up contraints for continuity

• connecting points of segments