Trajectorieswithout
Trajectorieswithout is a neologism in the field of dynamical systems and trajectory planning, used to denote a class of system trajectories that avoid a specified exclusion set. The concept emphasizes constraint satisfaction along the evolution of a system, rather than optimization of an objective alone.
Formally, consider a dynamical system x' = f(x,t) on a state space X, with a constraint or forbidden
Variants include trajectories that avoid multiple sets, or that avoid C while satisfying additional goals such
Computationally, trajectorieswithout arise in obstacle-avoiding motion planning, barrier-method optimization, and reachability analyses. Algorithms such as sampling-based
Applications span robotics, autonomous vehicles, and safety-critical systems where remaining outside unsafe or forbidden regions is