Controlling a Submerged Rigid Body: a Geometric Analysis

Monique Chyba (1) , Thomas Haberkorn (2) , Ryan N. Smith (3) , George Wilkens (1)

1 Department of Mathematics [Hawaii]
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 RESL - Robotics Embedded Systems Laboratory

In this paper we analyze the equations of motion of a submerged rigid body. Our motivation is based on recent developments done in trajectory design for this problem. Our goal is to relate some properties of singular extremals to the existence of decoupling vector elds. The ideas displayed in this paper can be viewed as a starting point to a geometric formulation of the trajectory design problem for mechanical systems with potential and external forces.

Keywords: Submerged Rigid Body; Decoupling Vector Fields; Singular Trajectories

Domains: Optimization and Control [math.OC]

Monique Chyba, Thomas Haberkorn, Ryan N. Smith, George Wilkens. Controlling a Submerged Rigid Body: a Geometric Analysis. 3rd IFAC Workshop, Jul 2006, Nagoya, Japan. pp. 375-386. ⟨hal-00444273⟩