Automatic path planning tasks in robotics can be modeled by suitable shortest path problems. A particular challenge is the computation of optimal paths in the presence of obstacles. For the detection of collisions of geometric bodies we use a linear programming approach, which exploits the Lemma of Gale.

The animation shows the automatic testdrive along a sloped road. The mathematical model is based on the single track model, which was augmented by dynamic tyre loads and force terms taking into account the longitudinal and lateral slope of the road. The trajectory was computed using OCPID-DAE1 using a model-predictive control scheme.

Automatic path planning tasks in robotics can be modeled by suitable optimal control problems. A particular challenge is the computation of optimal paths of robots that interact dynamically. We use multiple phases to model the maneuver, i.e. an approach phase, an interaction phase, and a return phase. This multiphase optimal control problem is then transformed by standard techniques to a single stage optimal control problem, which can be solved by a direct shooting method.

As the number of uncontrollable objects in low earth orbit is rising, the thread of collisions and thus the breakdown of working satellites becomes worth analyzing. Consequently, space debris removal becomes an issue. In this study an optimal docking maneuver of a service satellite to an uncontrolled tumbling target is modeled and solved numerically. After deriving the system dynamics, we introduce boundary conditions to ensure a safe and realizable maneuver and a general Bolza type cost functional to incorporate different optimization goals.

Modern vehicles offer a number of passive and active driver assistance systems, which shall support the driver in crucial situations. The degree of automation of such systems increases continuously and eventually ends in systems that act fully autonomously within given bounds. Such assistance systems get more and more important in controlling cars in all-day road traffic. In future cars will communicate and negotiate driving strategies. The following video illustrates a distributed model-predictive control algorithm for autonomous cars in typical traffic scenarios using car-to-car communication.

Data like position, velocity and heading are transmitted and shared among the vehicles. Regarding these informations a unique hierarchy level for each vehicle is derived according to predefined rules. Superordinate vehicles have to be considered for collision avoidance by vehicles with lower priority. Whereas vehicles with lower priority are neglected.

The Realtime Optimization and Control Simulator (ROCS) is a software package written in Qt3D with Unreal Engine frontend. It is being developped at the Engineering Mathematics Group of the Universität der Bundeswehr München. It is a versatile tool to visualize and control vehicles, aircrafts, and robots in complex scenarios.

The animation shows the flight of a UAV within a flight corridor. The flight path was computed by a nonlinear model-predictive control method for a point-mass model of a quadrocopter-like UAV.

The animation shows examples of a dynamic scheduling algorithm for automatic intersection management for autonomous cars. To this end a scheduling problems is coupled with optimal control subject to collision avoidance.

The video illustrates a finite state machine approach for automated driving developed by Mostafa Emam from the Engineering Mathematics Group of the Universität der Bundeswehr München. The corresponding paper was presented at VEHITS 2022. The approach is simulated in the 3D visualization environment ROCS with the aid of Omid Moslehirad.

The video illustrates an observation mission of a UAV with cloud avoidance. The flight path is generated by a model-predictive control technique. The approach is simulated in the 3D visualization environment ROCS and the unreal engine with the aid of Omid Moslehirad.

The video shows a landing maneuver of a UAV on a moving UGV. Both agents are controlled simultaneously by model-predictive control (MPC) in a cooperative way. The approach is simulated in the 3D visualization environment ROCS and the unreal engine with the aid of Omid Moslehirad.

The video shows a dynamic travelling salesman problem for a multi-agent system with time varying no-fly zones. The dynamic travelling salesman problem is a bi-level optimization problem coupling a multi-agent traveling salesman problem with optimal control problems for path planning.The approach is simulated in the 3D visualization environment ROCS and the unreal engine with the aid of Omid Moslehirad.

The video shows a dynamic routing problem with profits. This is a bi-level optimization problem coupling a routing problem with optimal control problems for path planning of multiple agents. The aim is to maximize profits within a given time frame. The approach is simulated in the 3D visualization environment ROCS and the unreal engine with the aid of Omid Moslehirad.

The video shows a landing maneuver of a UAV on a moving UGV using an online NMPC controller for the UAV. The communication is organized in ROS2 in realtime. The UGV communicates its predicted path to the UAV, which reacts on the motion of the UGV. The visualization is done by the unreal engine with the aid of Omid Moslehirad.

The video shows a docking maneuver of a service satellite with a mounted robotic arm to a tumbling target. The trajectory is generated by a bilevel dynamic programming approach with collision avoidance, which takes into account the geometry of the involved bodies. The results have been obtained within the dtec.bw project SeRANIS.

The video shows a docking maneuver of a service satellite with a mounted robotic arm to a tumbling target. The trajectory is generated by a reinforcement learning approach with collision avoidance, which takes into account the geometry of the involved bodies. The results have been obtained within the dtec.bw project SeRANIS.

The video shows the dynamic scheduling of drones with target assignment and collision avoidance. Dynamic scheduling combines scheduling with path planning and uses a bi-level optimization formulation. The results have been obtained by the Engineering Mathematics Group at the University of the Bundeswehr Munich.