# DLR Optimization LIBRARY

The Optimization library is fully integrated in Dymola to define and solve nonlinear multi-criteria parameter and trajectory optimization problems mainly based on simulations of Modelica models. The Optimization library offers several sophisticated numerical optimization algorithms for solving different kinds of optimization tasks. The library supports continuous and discrete parameters, several model operating points and optimal control problems. Computational performance of optimization runs is significantly increased by parallel simulations of the Modelica model on multicore machines or a computing cluster. The problem definition and the optimization process is interacitvely controlled by the user.

The library is commercially available at LTX and Dassault Systems.

## FEATURES OF THE LIBRARY

- Automatic simulation of a Modelica model with different model parameters
- Typical usage: model parameter identification, controller parameter optimization, parameter sweeps
- Multi criteria definitions

- Automatic simulation of a Modelica model in several operating points with different model parameters
- Combined model parameter identification for several operating points
- Combinded controller parameter optimization for several operating points
- Multi criteria definitions

- Automatic simulation of a Modelica model with different input signals (trajectories)
- Typical usage: optimal control problems, path optimization
- Multi criteria definitions

- GUI based optimization problem definition (free parameters/variables, criteria, scaling, numerical methods, …)
- Intermediate results during optimization run
- Graphical representation of several criteria

- Modelica criteria models
- Assess system performance or signal properties
- Direct usage in optimization models

- Parallel simulation of a Modelica model
- Different model parameter values for each run
- Support for multi-core machines and computing clusters

#### FEATURES OF THE LIBRARY

## APPLICATION EXAMPLES

One way to plan the path for the fastest robot’s movement is to solve a trajectory optimization problem with the inverse robot dynamics model that computes the motor torques from the robot’s motion. The constraints are defined by the maximum velocity and the maximum acceleration of the axis movements as well as the available maximum torque of the electrical motors. The definition and the solution of such a trajectory optimization problem can completely be handled by the Optimization library. |

In this example you can see two robots (unoptimized and optimized) that are moving a target object from the ground to the back of the DLR Lunar Rover Unit (LRU). The total energy consumption for that movement has to be decreased, it is displayed at the bottom. The optimized trajectory needs about 23% less energy compared to the non-optimized trajectory. This reduction is very important for space missions because energy is one of the most critical resources. The multi-criteria optimization makes sure that the trajectory is collision free and that ‘maximum peak’ torques of the robot joints are not exceeded. The total length of the trajectory is set to 14 seconds. |
## Trajectory Optimization of a Pick-Up Maneuver |