Intersection management using dynamic scheduling

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.

NMPC Flight Path Optimization of a UAV

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.

ROCS - Realtime Optimization and Control Simulator

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.

Distributed Model-Predictive Control with Car-to-Car Communication

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.

Docking Maneuver to a Tumbling Target

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.

Hierarchical Control of autonomous connected vehicles

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.

Automatic testdrive along a sloped road

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.

Dynamic Robot Interaction

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.

Collision Avoidance with KUKA youBot

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.