Constraint Violation Probability Minimization in Model Predictive Control

• Applicant: Dr.-Ing. Marion Leibold
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 490649198

Our goal is to enable Model Predictive Control approaches to cope with perception and modeling uncertainty. We want to develop methods that guarantee maximal robustness with respect to constraint admissibility while still ensuring availability of control solutions in critical situations. The developed methods are generic; however - for the sake of clarity - we use autonomous mobile robots and vehicles as demonstration platforms and argumentation examples. Control engineers are often faced with the challenge of having to control systems under the presence of temporally changing constraints. An example is the control of autonomous mobile robots navigating in the presence of other independently moving agents. A common control approach is to define cost functions that help selecting the most efficient behavior amongst all available actions. Constraints ensure that the system remains within allowed areas and does not conflict with other agents and their actions. With these cost functions and constraints, an optimal control problem can be solved that not only calculates efficient but also non-conflicting behavior. Since such behavior must be constantly updated with changes in the environment, Model Predictive Control (MPC) has proved to be the most suitable method to select and control robot behavior in dynamically changing environments. Robots in real-world environments are faced with uncertainty - in perception, action execution, and modeling. On the one hand, robust MPC methods are tailored to consider these uncertainties by making worst-case assumptions on these uncertainties and consider these worst-case scenarios during planning. Constraints are padded with a safety margin, which ensures that these constraints are not violated. However, this approach leads to a conservative selection of control inputs. While this strategy is appropriate in many standard situations, the limitation of admissible control inputs may cause the system to not find any solutions in critical situations with strongly limited action possibilities. In these situations, stochastic MPC may allow to the system to find solutions by relaxing hard constraints to chance constraints and allowing constraint violation with a certain probability. This strategy of bounding the probability of constraint violation enlarges the allowed control input space and increases the action capabilities of the system. In this project, we will develop a method that combines the advantages of robust worst-case MPC and stochastic chance constrained MPC. The obtained MPC approach maintains a robust safety margin to constraints whenever possible and seeks to minimize constraint violation probability in critical situations, thus, ensuring that the system remains active and a solution can be calculated.

• DFG Programme: Research Grants
• Co-Investigator: Privatdozent Dr.-Ing. Dirk Wollherr