Safety-Critical Autonomous Systems

The emergence of Autonomous Vehicles (AVs) and the need to guarantee safety in making them a reality has motivated us to develop a new framework adapting optimal control theory to safety-critical systems and demonstrating its use for AVs in signal-free traffic networks.

The standard trade-off we face in control system design is achieving a desired behavior without excessive computational complexity that would prohibit real-time applications. In autonomous systems as they have emerged, safety becomes such a crucial factor that we are often willing to sacrifice performance for the sake of safety, thus sometimes designing the system in an over-conservative manner. Therefore, in addition to trading off performance with computational complexity, the inclusion of hard constraint (safety) guarantees creates a new dimension in system design: the level of conservativeness in the control which also depends on the computational complexity we are willing to tolerate to achieve better performance and less conservativeness.

Most optimal control problems with hard constraints capturing “safety” quickly become intractable. Control Barrier Functions (CBFs) allow the derivation of sufficient conditions for these constraints with three key properties: (a) They transform the original state constraints (e.g., safe distances to avoid collisions) into constraints allowing us to derive explicit feedback controls that guarantee constraint satisfaction, (b) These transformed constraints are linear in the control/decision variables (as long as the dynamics involved are affine in the control but otherwise arbitrary), (c) They possess “forward invariance” in preserving safety. Thus, optimal control problem solutions can be obtained by discretizing time and solving a sequence of convex optimization problems (QPs) when the objective is quadratic). The solutions guarantee safety, but can become conservative. Moreover, these QPs can also become infeasible.

In a series of recent papers (and the book Xiao, W., Cassandras, C.G., and Belta, C., “Safe Autonomy with Control Barrier Functions: Theory and Applications”, 2023), our research has shown that:

  • Updating the control in an event-driven manner (rather than time-driven) eliminates all infeasibility cases due to inter-sampling effects caused by time-driven updates.
  • The rest of infeasible cases are due to conflicts between CBF constraints and control/decision limits. These can also be eliminated by identifying additional constraints that ensure the prevention of such conflicts.
  • Developing adaptive CBFs enables the use of these methods to time-varying environments, as well as to guarantee that when agents are outside a safe set their state can converge to the safe set in finite time.
  • Event-triggered CBFs allow the use of these methods to autonomous multi-agent systems where the agent dynamics are unknown. This opens up the opportunity to develop model-free methods for the control and optimization of autonomous multi-agent systems.
  • These new methods have been applied to Autonomous Vehicles (AVs), including a project where they were implemented on an actual AV (NEXTCAR – see picture) and tested in the Mcity facility (Ann Arbor, Michigan). The assumption so far, however, is that all vehicles in a transportation network are AVs. This needs to be relaxed!
  • Ongoing work is now leading to new results for (cooperating) AVs that must co-exist with (uncooperative) human-driven vehicles. In a broader setting, this creates a game environment where cooperating agents can form coalitions to counteract the unpredictable behavior of uncooperative agents. Some of these new results are surprising and promising, e.g., Li, A., Chavez Armijos, A., and Cassandras, C.G., “Cooperative Lane Changing in Mixed Traffic can be Robust to Human Driver Behavior”, Proc. of 62nd IEEE Conference on Decision and Control, 2023.