task-scaling sqp controller

This work addresses the challenge of generating safe, dynamically feasible flight trajectories in real time for high-density urban low-altitude environments. The authors propose a scalable sequential quadratic programming (SQP) framework that unifies environmental geometric constraints, operational limits, and full six-degree-of-freedom aircraft dynamics into a single optimization model. A key innovation lies in dynamically generating separating hyperplanes during each SQP iteration to enable immediate collision avoidance, while a variable-resolution quadtree spatial decomposition ensures real-time performance even in large-scale urban scenarios. Experimental results across five real-world city environments demonstrate 100% mission success and guaranteed collision avoidance using only CPU computation, significantly outperforming conventional approaches such as standard SQP, iterative Linear Quadratic Regulator (iLQR), and Differential Dynamic Programming (DDP).

Addressing the challenges of difficult hyperparameter tuning and slow convergence in convex quadratic programming (QP) solvers, this paper introduces, for the first time, a reinforcement learning–based approach to the stabilized interior-point method (IPM). We propose a novel double-loop online adaptive hyperparameter control framework: an outer loop employs a policy network to dynamically adjust key IPM parameters—including damping factors and step-size scaling—while the inner loop performs standard numerical optimization iterations. The method requires no problem-specific prior knowledge and exhibits strong generalization across diverse QP problem classes and dimensions. Empirical evaluation demonstrates that, under lightweight training, the learned policy significantly reduces time-to-high-accuracy solutions, achieving average speedups of 1.8–3.2× over baseline solvers on QP instances of varying scales. Moreover, it outperforms conventional heuristics and Bayesian optimization in robustness and adaptability.

为解决机器人控制中QP求解器因约束冲突导致的不可行问题，提出ElastiQP算法，通过引入l1惩罚项并保持线性系统规模不变，确保快速获得可行解。

This work addresses discrete-time nonlinear optimal control problems by unifying classical algorithms—including gradient descent, Gauss–Newton, Newton’s method, and differential dynamic programming (DDP)—within a differentiable programming framework. Methodologically, it introduces the first modular, end-to-end differentiable algorithm template library built upon linear/quadratic approximations (e.g., LQR), enabled by automatic differentiation. Theoretically, it provides a unified derivation of computational complexity and sufficient optimality conditions across all methods. Practically, it incorporates adaptive line search and regularization strategies, and validates efficacy on benchmark tasks such as autonomous racing with a bicycle model. All implementations are open-sourced, demonstrating both efficient gradient propagation and strong generalization across diverse control problems.

Mapping and scheduling workloads on HPC heterogeneous systems is NP-hard, while high-speed robotic contact tasks suffer from control instability due to 3D frictional impact dynamics. Method: This paper proposes an impact-aware task-space quadratic programming (QP) control framework. It explicitly models impact events within the task-space QP formulation for the first time, incorporating hardware-admissible impact boundaries and an analytically derived post-impact state feasibility set—represented as polyhedral constraints—alongside a one-step preview mechanism and online constraint reconfiguration to ensure robust contact control under uncertain impact timing and location. The approach integrates impact dynamics modeling, polyhedral feasible-set analysis, and real-time state-constraint reprojection. Results: Experiments demonstrate significantly improved moderate-impact robustness on a Panda manipulator and successful high-speed grasping on an HRP-4 humanoid robot, with substantial suppression of joint torque and velocity transients during impact.

This work addresses the limitation of existing safe ergodic control methods, which rely on offline optimization and decouple ergodic objectives from safety constraints, thereby hindering real-time deployment. We propose a quadratic programming (QP)-based real-time cooperative monitoring controller for multi-robot systems. A key innovation is the introduction of a time-differentiable Gaussian kernel ergodic metric, whose exponential decay property is reformulated as a time-varying control barrier function constraint to enable the joint optimization of ergodicity and safety. The feasibility of the QP formulation and the exponential convergence of the metric are rigorously proven in theory. Simulation results demonstrate superior performance compared to baseline methods, and the effectiveness of the proposed approach is further validated through hardware experiments on a three-UAV platform.

This work addresses the limited real-time scalability of traditional linear-quadratic (LQ) control, which relies on sequential dynamic programming and cannot exploit the parallel processing capabilities of modern multi-core CPUs. To overcome this bottleneck, the authors propose a novel time-parallel method that, for the first time, integrates the Riccati recursion with the alternating direction method of multipliers (ADMM). By decomposing the time domain, the approach partitions constrained optimal control problems—specifically those with conic constraints—into smaller LQ subproblems that can be solved in parallel. Each subproblem is efficiently handled via dynamic programming. The resulting framework breaks the serial dependency inherent in classical solvers and achieves up to a 5× speedup on multi-core CPUs in two real-world scenarios, demonstrating significant gains in computational efficiency without compromising solution accuracy.

This work proposes an efficient real-time nonlinear model predictive control (NMPC) approach for the remote underactuated double pendulum system under unknown parameters and limited interaction time. By integrating a structure-exploiting alternating direction method of multipliers (ADMM) with an interior-point-accelerated sequential quadratic programming (SQP) solver, the method achieves global swing-up and stabilization without requiring prior model knowledge. The proposed framework is directly deployed on the CloudPendulum remote hardware platform, satisfying stringent real-time constraints while demonstrating strong robustness and disturbance rejection capabilities. Experimental results confirm its effectiveness in reliably achieving both swing-up and stable regulation of the double pendulum system.

This work addresses the high computational burden of nonlinear model predictive control (NMPC), which requires solving a constrained nonlinear program online and is thus challenging to deploy on resource-constrained or high-sample-rate systems. Focusing on input-affine nonlinear systems, the authors propose an efficient approximation scheme that models the optimal control law as a state-dependent quadratic program (QP) and introduces a single-network residual correction architecture to learn the discrepancy between the QP solution and the true nonlinear programming (NLP) solution. A differentiable interior-point optimization layer is embedded to guarantee constraint satisfaction for the first control step, and the network is trained jointly using a hybrid loss combining supervised imitation learning and KKT residual minimization. Evaluated on a three-link robotic arm trajectory tracking task, the method achieves an order-of-magnitude speedup over the original NLP solver while maintaining comparable tracking accuracy.

This work addresses the challenge of autonomous driving motion planning under real-time constraints, requiring a balance among safety, rule compliance, comfort, and efficiency while enabling auditable decision-making. The authors propose W-SQP, a nonlinear model predictive controller based on weighted hierarchical slack variables, which encodes nine categories of driving rules into a four-layer nonlinear program with shared slack variables. A strongly separated hierarchical penalty mechanism prioritizes satisfaction of higher-priority rules while preserving hard actuator constraints. Leveraging CasADi and IPOPT, the system solves the optimization problem online at 10 Hz, guaranteeing feasible solutions at every time step and logging rule residuals for auditability. In closed-loop evaluations across 150 scenarios from the Waymo Open Motion Dataset, the method exhibits no systematic failures in safety or compliance metrics, with only localized performance degradation observed in highly ambiguous, complex scenes.