Matthias Gerdts

About

Matthias Gerdts is a prominent applied mathematician and control engineer whose research sits at the intersection of optimal control theory, robotics, and autonomous systems. His most influential contributions center on trajectory optimization and collision avoidance, particularly developing mathematically rigorous frameworks for guiding robots and vehicles through complex, obstacle-laden environments. His 2012 paper on path planning and collision avoidance for robots, which garnered 56 citations, established a foundational optimal control formulation using linear programming arguments to generate the fastest collision-free trajectories—an approach he subsequently extended to welding robots and automotive applications. Gerdts has made significant methodological contributions through his development of nonsmooth Newton's methods for solving discretized optimal control problems with state and control constraints, earning 41 citations and providing practitioners with powerful numerical tools. His work on linear model-predictive control for mobile robots, bilevel optimal control, and reachable set computation further demonstrates his breadth across theoretical and applied domains. More recently, he has tackled multi-agent scenarios involving interacting vehicles using generalized Nash equilibrium frameworks. Through differential-algebraic equation modeling and sensitivity-based real-time control strategies, Gerdts continues advancing the mathematical foundations essential for safe, efficient autonomous systems in industrial and automotive settings.

Research Focus

Key Achievements

Top Papers

1. 1
   Path planning and collision avoidance for robots

   56 citations · 2012
2. 2
   A nonsmooth Newton's method for discretized optimal control problems with state and control constraints

   41 citations · 2008
3. 3
   A Nonsmooth Newton Method for Linear Model-Predictive Control in Tracking Tasks for a Mobile Robot With Obstacle Avoidance

   34 citations · 2020
4. 4
   DAE Aspects in Vehicle Dynamics and Mobile Robotics

   11 citations · 2018
5. 5
   Numerical Approaches Towards Bilevel Optimal Control Problems with Scheduling Tasks

   11 citations · 2017
6. 6
   Optimization-based subdivision algorithm for reachable sets

   8 citations · 2020
7. 7
   Path-Planning with Collision Avoidance in Automotive Industry

   8 citations · 2013
8. 8
   Control of interacting vehicles using model-predictive control, generalized Nash equilibrium problems, and dynamic inversion

   5 citations · 2020
9. 9
   Neighborhood estimation in sensitivity-based update rules for real-time optimal control

   4 citations · 2020
10. 10
    Collision-Free Path Planning of Welding Robots

    2 citations · 2014

Key Collaborators

Contact & Links