Automated vehicles require efficient and safe planning to maneuver in uncertain environments. Largely this uncertainty is caused by other traffic participants, e.g., surrounding vehicles. Future motion of surrounding vehicles is often difficult to predict. Whereas robust control approaches achieve safe, yet conservative motion planning for automated vehicles, Stochastic Model Predictive Control (SMPC) provides efficient planning in the presence of uncertainty. Probabilistic constraints are applied to ensure that the maximal risk remains below a predefined level. However, safety cannot be ensured as probabilistic constraints may be violated, which is not acceptable for automated vehicles. Here, we propose an efficient trajectory planning framework with safety guarantees for automated vehicles. SMPC is applied to obtain efficient vehicle trajectories for a finite horizon. Based on the first optimized SMPC input, a guaranteed safe backup trajectory is planned using reachable sets. This backup is used to overwrite the SMPC input if necessary for safety. Recursive feasibility of the safe SMPC algorithm is proved. Highway simulations show the effectiveness of the proposed method regarding performance and safety.

Autonomous vehicles face the challenge of providing safe transportation while efficiently maneuvering in an uncertain environment. Considering surrounding vehicles, two types of uncertainties occur: multiple future maneuvers are possible, and within these maneuvers the vehicle can vary from the predicted ideal maneuver path. Focusing on only one of these uncertainties can either lead to neglecting potential risks or result in overly conservative motion planning. Here, we suggest a Stochastic Model Predictive Control strategy that tackles the possibility of multiple future maneuvers of surrounding vehicles, while also considering uncertainty within the execution of these predicted maneuvers. The proposed control method is a combination of Scenario Model Predictive Control to cope with multiple predicted maneuvers of other vehicles, and Stochastic Model Predictive Control using chance-constraints to take into account vehicle deviations from the predicted maneuver trajectories of the respective maneuver. Adjustable risk parameters permit a violation of safety constraints up to a desired probability, allowing a trade-off between risk and performance. A simulation of a two-lane scenario demonstrates the effectiveness of our method.

A powerful result from behavioral systems theory known as the fundamental lemma allows for predictive control akin to Model Predictive Control (MPC) for linear time-invariant (LTI) systems with unknown dynamics purely from data. While most data-driven predictive control literature focuses on robustness with respect to measurement noise, only a few works consider exploiting probabilistic information of disturbances for performance-oriented control as in stochastic MPC. This work proposes a novel data-driven stochastic predictive control scheme for chance-constrained LTI systems subject to measurement noise and additive stochastic disturbances. In order to render the otherwise stochastic and intractable optimal control problem deterministic, our approach leverages ideas from tube-based MPC by decomposing the state into a deterministic nominal state driven by inputs and a stochastic error state affected by disturbances. Satisfaction of original chance constraints is guaranteed by tightening nominal constraints probabilistically with respect to additive disturbances and robustly with respect to measurement noise. The resulting data-driven receding horizon optimal control problem is lightweight, recursively feasible, and renders the closed loop input-to-state stable in the presence of both additive disturbances and measurement noise. We demonstrate the effectiveness of the proposed approach in a simulation example.

For Model Predictive Control in safety‐critical systems it is not only important to bound the probability of constraint violation but to reduce this constraint violation probability as much as possible. Therefore, an approach is necessary that minimizes the constraint violation probability while ensuring that the Model Predictive Control optimization problem remains feasible even under changing uncertainty. We propose a novel two‐step Model Predictive Control scheme that yields a solution with minimal constraint violation probability for a norm constraint in an environment with uncertainty. After minimal constraint violation is guaranteed, the solution is then also optimized with respect to other control objectives. Recursive feasibility and convergence of the method are proved. A simulation demonstrates the effectiveness of the proposed method for a collision avoidance example.

Solving chance-constrained stochastic optimal control problems is a significant challenge in control. This is because no analytical solutions exist for up to a handful of special cases. A common and computationally efficient approach for tackling chance-constrained stochastic optimal control problems consists of a deterministic reformulation, where hard constraints with an additional constraint-tightening parameter are imposed on a nominal prediction that ignores stochastic disturbances. However, in such approaches, the choice of constraint-tightening parameter remains challenging, and guarantees can mostly be obtained assuming that the process noise distribution is known a priori. Moreover, the chance constraints are often not tightly satisfied, leading to unnecessarily high costs. This work proposes a data-driven approach for learning the constraint-tightening parameters online during control. To this end, we reformulate the choice of constraint-tightening parameter for the closed loop as a binary regression problem. We then leverage a highly expressive Gaussian process, model for binary regression to approximate the smallest constraint-tightening parameters that satisfy the chance constraints. By tuning the algorithm parameters appropriately, we show that the resulting constraint-tightening parameters satisfy the chance constraints up to an arbitrarily small margin with high probability. Our approach yields constraint-tightening parameters that tightly satisfy the chance constraints in numerical experiments, resulting in a lower average cost than three other state-of-the-art approaches.

Stochastic Model Predictive Control (SMPC) has attracted increasing attention for autonomous driving in recent years, since it enables collision-free maneuvers and trajectory planning and can deal with uncertainties in a non-conservative way. Many promising strategies have been proposed on how to use SMPC to select appropriate maneuvers and plan safe trajectories in uncertain environments. The limitation of these approaches is that they focus on scenarios where only one vehicle is controlled by SMPC and is, thus, reacting to the surrounding vehicles; however, the surrounding vehicles do not react to the SMPC-controlled vehicle, which means there is no mutual interaction. However, when multiple autonomous vehicles are driving on the road, each individual vehicle will take the behavior of the other surrounding vehicles into account and adjust its individual decisions accordingly in trajectory planning. This paper, therefore, examines in simulations how the interactive control system of multiple SMPC-controlled vehicles behave based on a Distributed SMPC (DSMPC) framework. For a three-lane highway scenario, we first investigate the effects of the risk parameter of the collision avoidance probabilistic constraint on non-interactive and interactive vehicle systems and provide insights into how to parameterize the controllers in interactive vehicle systems.