A metric modification approach to control
 
 
Description: 

Control theory plays a fundamental role in the modeling and trajectory planning of actuated dynamical systems. In recent decades, the use of differential geometric methods, namely Lagrangian and Hamiltonian mechanics, has become prevalent within the control theory literature due to the intrinsic descriptions and natural connections to optimal control problems that they offer. However, stability analysis remains challenging due to the non-canonical nature of configuration errors, and the construction of suitable Lyapunov functions. Additionally, the complex interdependencies between control gains and the need for state-of-the-art numerical integrators on manifolds have further complicated practical implementation. In this talk, I will introduce a novel approach that reformulates control problems within the framework of Riemannian geometry by selectively designing control forces that can be incorporated into the system's underlying Riemannian metric (kinetic energy). This perspective allows system trajectories to be interpreted as geodesics with respect to a modified metric, unlocking analytical tools from Riemannian geometry that are typically unavailable in Geometric Control Theory. Additionally, these metric modifications can be designed to complete tasks such as obstacle avoidance, flocking, and trajectory-tracking while also facilitating the development of robust numerical integrators for simulating dynamical systems on manifolds.

Date:  2025-03-19
Start Time:   14:30
Speaker:  Jacob Goodman (Univ. Nebrija, Madrid, Spain)
Institution:  University of Nebrija, Spain
Place:  Sala 5.5, DMUC
Research Groups: -Geometry
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