The cart-pole swing-up is a canonical benchmark for nonlinear control of underactuated systems, yet an end-to-end guarantee linking the global swing-up maneuver to the local stabilizer is seldom formalized. We present a reachability analysis of a switched energy-based/LQR controller that certifies convergence to the upright equilibrium from a compact set of initial conditions. The swing-up law is derived from an energy-error Lyapunov function; canceling the autonomous conservative term yields a strictly sign-definite Lyapunov derivative, and convergence follows from LaSalle's invariance principle. We also propose an augmented Lyapunov function to regulate the steady-state cart velocity to zero, for which we establish almost-global convergence. For the controller handoff, a switching region is designed to lie strictly within the LQR region of attraction, formally certifying the swing-up-to-stabilization transition. Numerical simulations corroborate the theoretical analysis.
Fully actuated unmanned aerial vehicles (UAVs) are usually certified through rank conditions on a control-allocation matrix or through free-flight tracking performance. For aerial physical interaction, this certification may be incomplete. During sustained contact, part of the av…
This paper presents a method for computing inner polytopic approximations of admissible sets for continuous-time linear control systems subject to affine state constraints. Building upon barrier theory and the explicit solution of linear systems, a structured sampling procedure i…
Cable-Driven Parallel Robots (CDPRs) are a type of parallel mechanism in which cables are used as actuators. Due to the two levels of redundancy and numerous constraints within the CDPR actuation, joint and operational spaces (together known as the tri-space), tracking a given tr…
Deploying drone swarms to track a dynamic target in cluttered environments presents severe computational and safety challenges. We propose MROPE, a hierarchical strategy that decouples the cooperative monitoring mission from strict local safety requirements. To overcome the compu…
This article presents a modular inference framework that integrates Flow Matching generative models with formal Control Barrier Function (CBF) safety guarantees. Unlike existing methods that apply external safety filters to a model's final output, our approach modifies the Flow M…
Different Length Alignment Sewing (DLAS), which involves stretching the shorter fabric to match the longer one and sewing them together in a straight line, is a challenging task that needs to satisfy several requirements when automating the sewing process. To address the challeng…