We thank all reviewers for their encouraging and helpful comments. We will fix all typos. Results are presented in Table A. Following convex relaxation theory[32], our bound has This makes the concretization problem (in Sec. We plan to study high-order bounds on general graphs as our future work. We will also discuss these extensions.

Abstract--This work presents an event-triggered switching control framework for a class of nonlinear underactuated multi-channel systems with input constraints. These systems are inspired by cooperative manipulation tasks involving underactua-tion, where multiple underactuated agents collaboratively push or pull an object to a target pose. T o simultaneously account for channel assignment, input constraints, and stabilization, we formulate the control problem as a Mixed Integer Linear Programming and derive sufficient conditions for its feasibility. T o improve real-time computation efficiency, we introduce an event-triggered control scheme that maintains stability even between switching events through a quadratic programming-based stabilizing controller . We theoretically establish the semi-global exponential stability of the proposed method and the asymptotic stability of its extension to nonprehensile cooperative manipulation under noninstantaneous switching. The proposed framework is further validated through numerical simulations on 2D and 3D free-flyer systems and multi-robot nonprehensile pushing tasks. Cooperative tasks involving objects that are collectively controlled by multiple agents such as drone swarms and robotic arms in manufacturing rely on precise object manipulation.

Large language Models (LLMs) have shown remarkable proficiency in code generation tasks across various programming languages. However, their outputs often contain subtle but critical vulnerabilities, posing significant risks when deployed in security-sensitive or mission-critical systems. This paper introduces TypePilot, an agentic AI framework designed to enhance the security and robustness of LLM-generated code by leveraging strongly typed and verifiable languages, using Scala as a representative example. We evaluate the effectiveness of our approach in two settings: formal verification with the Stainless framework and general-purpose secure code generation. Our experiments with leading open-source LLMs reveal that while direct code generation often fails to enforce safety constraints, just as naive prompting for more secure code, our type-focused agentic pipeline substantially mitigates input validation and injection vulnerabilities. The results demonstrate the potential of structured, type-guided LLM workflows to improve the SotA of the trustworthiness of automated code generation in high-assurance domains.

Verifying the safety of controllers is critical for many applications, but is especially challenging for systems with bounded inputs. Backup control barrier functions (bCBFs) offer a structured approach to synthesizing safe controllers that are guaranteed to satisfy input bounds by leveraging the knowledge of a backup controller. While powerful, bCBFs require solving a high-dimensional quadratic program at run-time, which may be too costly for computationally-constrained systems such as aerospace vehicles. We propose an approach that optimally interpolates between a nominal controller and the backup controller, and we derive the solution to this optimization problem in closed form. We prove that this closed-form controller is guaranteed to be safe while obeying input bounds. We demonstrate the effectiveness of the approach on a double integrator and a nonlinear fixed-wing aircraft example.

This article proposes a periodic event-triggered adaptive barrier control policy for the trajectory tracking problem of perturbed Euler-Lagrangian systems with state, input, and temporal (SIT) constraints. In particular, an approximation-free adaptive-barrier control architecture is designed to ensure prescribed-time convergence of the tracking error to a prescribed bound while rejecting exogenous disturbances. In contrast to existing approaches that necessitate continuous real-time control action, the proposed controller generates event-based updates through periodic evaluation of the triggering condition. Additionally, we derive an upper bound on the monitoring period by analysing the performance degradation of the filtered tracking error to facilitate periodic evaluation of the event-triggered strategy. To this end, a time-varying threshold function is considered in the triggering mechanism to reduce the number of triggers during the transient phase of system behaviour. Notably, the proposed design avoids Zeno behaviour and precludes the need for continuous monitoring of the triggering condition. A simulation and experimental study is undertaken to demonstrate the efficacy of the proposed control scheme.

Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search, as they achieve good predictive performance with little or no manual tuning, naturally handle discrete feature spaces, and are relatively insensitive to outliers in the training data.

In this paper, we present a novel funnel-based tracking control algorithm for robotic systems with unknown dynamics and prescribed input constraints. The Euler-Lagrange formulation, a common modeling approach for robotic systems, has been adopted in this study to address the trade-off between performance and actuator safety. We establish feasibility conditions that ensure tracking errors evolve within predefined funnel bounds while maintaining bounded control efforts, a crucial consideration for robots with limited actuation capabilities. We propose two approximation-free control strategies for scenarios where these conditions are violated: one actively corrects the error, and the other stops further deviation. Finally, we demonstrate the robust performance and safety of the approach through simulations and experimental validations. This work represents a significant advancement in funnel-based control, enhancing its applicability to real-world robotics systems with input constraints.

Figure 1: This paper introduces BLAZE, a Phase 1 - Phase 2 Affine Geometric Heat Flow (AGHF) framework, to rapidly solve optimal control problems while respecting robot constraints and avoiding obstacles. It begins with an initial trajectory (shown in orange with the color gradient illustrating the evolution in time starting from darkest and going to lightest) that may violate constraints (e.g., the second and fourth pose of the arm are in collision with the boxes and outlined in red). If the initial trajectory is infeasible, BLAZE enters Phase 1, where it evolves the trajectory into a trajectory that satisfies all constraints (e.g., in the blue trajectory, the Kinova arm has been moved out of collision with the boxes). Once the trajectory satisfies all constraints, Phase 2 begins, optimizing the motion to minimize a user-specified cost function while maintaining feasibility (optimized trajectory shown green). BLAZE optimizes the trajectory to reach a target configuration while avoiding the obstacles while considering the full dynamical model of the arm. Note that optimal control (including Phase 1 and Phase 2) for this 14 dimensional state space model is completed within 3s while satisfying input, state, and collision avoidance constraints. Abstract --The generation of optimal trajectories for high-dimensional robotic systems under constraints remains computationally challenging due to the need to simultaneously satisfy dynamic feasibility, input limits, and task-specific objectives while searching over high-dimensional spaces. Recent approaches using the Affine Geometric Heat Flow (AGHF) Partial Differential Equation (PDE) have demonstrated promising results, generating dynamically feasible trajectories for complex systems like the Digit V3 humanoid within seconds. These methods efficiently solve trajectory optimization problems over a two-dimensional domain by evolving an initial trajectory to minimize control effort. However, these AGHF approaches are limited to a single type of optimal control problem (i.e., minimizing the integral of squared control norms) and typically require initial guesses that satisfy constraints to ensure satisfactory convergence. These limitations restrict the potential utility of the AGHF PDE especially when trying to synthesize trajectories for robotic systems. This paper generalizes the AGHF formulation to accommodate arbitrary cost functions, significantly expanding the classes of trajectories that can be generated. This work also introduces a Phase 1 - Phase 2 Algorithm that enables the use of constraint-violating initial guesses while guaranteeing satisfactory convergence. The effectiveness of the proposed method is demonstrated through comparative evaluations against state-of-the-art techniques across various dynamical systems and challenging trajectory generation problems. Optimal Control is a powerful tool for motion planning and control of advanced robotic systems.