Sequential feasibility and constraint properties of CAV platoons under various vehicle dynamics and safety distance constraints

Connected and autonomous vehicle (CAV) platooning technologies have been extensively studied. Many CAV platoon control schemes, e.g., model predictive control schemes, are formulated as constrained optimization problems since they can effectively handle vehicle dynamics, physical and safety constraints, and desired performance. At each time, a control input is generated from a constrained optimization problem, whose constraint set is time-varying and depends on states and controls in the past times. A fundamental question is whether the underlying optimization problem is sequentially feasible, i.e., whether the constraint set is nonempty at each time along a platoon state solution, assuming that it starts from an arbitrary initial condition which satisfies the physical and safety distance constraints. In this paper, we present a comprehensive study of sequential feasibility and related constraint properties under various vehicle dynamics and safety distance constraints. In particular, we consider three types of linear or nonlinear vehicle dynamic models and a wide range of representative spacing policy based safety distance constraints as well as physical constraints. We show that the constant spacing based safety distance constraint does not yield sequential feasibility, whereas most of variable spacing policy based safety distance constraints, along with the physical constraints, ensure sequential feasibility under mild, easily verifiable conditions on constraint or vehicle dynamics parameters. Extensions to general and unified forms of safety distance constraints have been made. We also show that under additional assumptions, each non-polyhedral constraint set has nonempty interior if sequential feasibility holds. This constraint property plays an important role in robust sequential feasibility analysis and optimization algorithm development.