Problem Formulation
Problem Formulation
Embedded Files
Cost Function Formulation
Cost Function Formulation
In the current scenario, a CAV seeks to navigate the curved road illustrated in Figure 1.
We model the CAV using double integrator dynamics, taking into account the longitudinal motion and fixing the lateral motion along the trajectory.
The control input is the longitudinal acceleration.
The CAV's dynamics can be described as:
where k is the discrete-time integer index, T is the size of the discrete-time step in seconds, p(k) is the longitudinal position, v(k) is the longitudinal speed, and u(k) is the longitudinal acceleration at time k.
The desired driving speed is a function of the CAV’s position, p(k), given by:
The objective of this control problem is to minimize the combination of three sub-objectives:
a. Normalized minimization of deviation from desired speed.
b. Normalized minimization of longitudinal jerk.
c. Normalized prioritization of turning comfort (coupling of longitudinal and lateral accelerations with an n-norm).
The objective function is a weighted sum of each of these sub-objectives.
Given a passenger's language input on their preferences, the LLM must select the 2 desired driving speeds and the 3 weights.
Subsequently, we implement model-predictive control to solve this problem, providing the acceleration profile and final trajectory to the CAV.
Simple Double Integrator Dynamics
Simple Double Integrator Dynamics
Figure 1
Geometry of the road environment:
- Initial position p(0): 0.0 m
- Initial velocity v(0): 0.0 m/s
- Initial acceleration u(0): 0.0 m/s^2
- Speed limit: 35.0 m/s
- Length l of straight paths: 1000.0 m
- Radius d of the curve: 150.0 m
- Total length of road segment: 2236.0 m
- Width of the lane: 4.0 m
- Angle of the curve: 90 degrees
Author of the Page: Shruti Banerjie
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