Techniques are discussed for generating and optimizing a trajectory using closed-form numerical integration in route-relative coordinates. A decision planner component of an autonomous vehicle, for example, can receive or generate a reference trajectory, which may correspond to an ideal route for an autonomous vehicle to traverse through an environment, such as a center of a road segment. Lateral dynamics (e.g., steering angles, curvature values of trajectory segments) and longitudinal dynamics (e.g., velocity and acceleration) can be represented in a single algorithm such that optimizing the reference trajectory (e.g., based on loss functions or costs) can substantially simultaneously optimize the lateral dynamics and longitudinal dynamics in a single convergence operation. In some cases, the trajectory can be used to control the autonomous vehicle to traverse an environment.