4 papers
Optimal Decay Matrix Control Barrier Functions: Soundness and Completeness for Matrix Safety Constraints
Samuel G. Gessow, Albert Wu, Aaron D. Ames +1
Many safety requirements, such as keeping a manipulator away from kinematic singularities, a network connected, or a system observable, amount to keeping a state-dependent matrix p…
High-Order Matrix Control Barrier Functions: Well-Posedness and Feasibility via Matrix Relative Degree
Samuel G. Gessow, Pio Ong, Aaron D. Ames +1
Control barrier functions (CBFs) provide an effective framework for enforcing safety in dynamical systems with scalar constraints. However, many safety constraints are more natural…
Analysis of the Geometric Heat Flow Equation: Computing Geodesics in Real-Time with Convergence Guarantees
Samuel G. Gessow, Brett T. Lopez
We present an analysis on the convergence properties of the so-called geometric heat flow equation for computing geodesics (extremal curves) on Riemannian manifolds. Computing geod…
Two-Impulse Trajectory Design in Two-Body Systems With Riemannian Geometry
Samuel G. Gessow, James Tseng, Eden Zafran +1
This work presents a new method for generating impulsive trajectories in restricted two-body systems by leveraging Riemannian geometry. The proposed method transforms the standard…