Thomas Meurer

Max Lutz, Thomas Meurer

To be applicable to real world scenarios trajectory planning schemes for mobile autonomous systems must be able to efficiently deal with obstacles in the area of operation. In the context of optimization based trajectory planning and control a number of different approaches to formulate collision avoidance constraints can be found in the literature. Here the contribution of the present work is twofold. First, the most popular methods to represent obstacles are summarized, namely the simple ellipsoidal representation, the constructive solid geometry (CSG) method as well as a direct and an indirect implementation of a signed distance based approach. The formulations are characterized with respect to the impact on the complexity of the optimization problem, as well as the ability to meet different problem requirements. Second, this work presents a novel variant of the CSG method to describe collision avoidance constraints. It is highly efficient due to a very low number of nonlinear inequality constraints required for a given number of obstacles and sample points and in contrast to the original CSG formulation allows to consider the controlled system's shape. The good performance of the proposed formulation is demonstrated by a comparison to the previously mentioned alternatives. To this end optimal trajectory planning for marine surface vessels formulated as a nonlinear programming problem is used as a benchmark example where the scenario is designed based on the maritime test field in Kiel, Germany.

Simon Helling, Christian Roduner, Thomas Meurer

A path-following collision-avoidance model predictive control (MPC) method is proposed which approximates obstacle shapes as convex polygons. Collision-avoidance is ensured by means of the signed distance function which is calculated efficiently as part of the MPC problem by making use of a dual formulation. The overall MPC problem can be solved by standard nonlinear programming (NLP) solvers. The dual signed distance formulation yields, besides the (dual) collision-avoidance constraints, norm, and consistency constraints. A novel approach is presented that combines the arising norm equality with the dual collision-avoidance inequality constraints to yield an alternative formulation reduced in complexity. Moving obstacles are considered using separate convex sets of linearly predicted obstacle positions in the dual problem. The theoretical findings and simplifications are compared with the often-used ellipsoidal obstacle formulation and are analyzed with regard to efficiency by the example of a simulated path-following autonomous surface vessel during a realistic maneuver and AIS obstacle data from the Kiel bay area.

Manuel Amersdorfer, Thomas Meurer

We present a cost-efficient and versatile method to map an unknown 3D freeform surface using only sparse measurements while the end-effector of a robotic manipulator moves along the surface. The geometry is locally approximated by a plane, which is defined by measured points on the surface. The method relies on linear Kalman filters, estimating the height of each point on a 2D grid. Therefore, the approximation covariance for each grid point is determined using a radial basis function to consider the measured point positions. We propose different update strategies for the grid points exploiting the locality of the planar approximation in combination with a projection method. The approach is experimentally validated by tracking the surface with a robotic manipulator. Three laser distance sensors mounted on the end-effector continuously measure points on the surface during the motion to determine the approximation plane. It is shown that the surface geometry can be mapped reasonably accurate with a mean absolute error below 1 mm. The mapping error mainly depends on the size of the approximation area and the curvature of the surface.

Petro Feketa, Alexander Schaum, Thomas Meurer et al.

The paper develops new sufficient conditions for synchronization of a network of $N$ nonlinearly coupled Chua oscillators interconnected via the first state coordinate only. The nonlinear coupling strength is governed by a function residing within a sector, i.e. it is bounded from above and below by linear functions. The derived sufficient conditions provide a trade-off between the characteristics of the sector and the interconnection topology of the network to guarantee the synchronization of the oscillators.