qp-relaxed dfl

This work addresses the singularity issue in dynamic feedback linearization (DFL) for single-wheel robot trajectory tracking, which arises at zero velocity and prevents maneuvers such as stopping and reversing. To overcome this limitation, the authors propose an optimal control framework based on quadratic programming (QP). By introducing slack variables, the DFL constraints are reformulated into a QP problem with equality constraints, and tunable parameters are incorporated to ensure feasibility for any system state and reference trajectory while preserving local Lipschitz continuity of the feedback law. The approach effectively eliminates the zero-velocity singularity, thereby expanding the range of admissible trajectories without compromising theoretical rigor or practical applicability. High-fidelity simulations on the TurtleBot3 Waffle platform within a ROS 2–Gazebo environment demonstrate precise trajectory tracking performance, including during stop-and-reverse maneuvers.

This work proposes a constraint-aware quadratic programming (QP) control framework for end-effector trajectory tracking of underactuated aerial manipulators under safety and feasibility constraints. The approach explicitly incorporates underactuated dynamics, actuator saturation, and system constraints to directly compute physically feasible generalized accelerations. It innovatively integrates passivity-based integral action at the torque level to enhance robustness against modeling errors and external disturbances. High-fidelity simulations demonstrate that the method achieves high-precision trajectory tracking, smooth control inputs, and reliable constraint satisfaction even in the presence of parameter perturbations, joint friction, and realistic sensing conditions.

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 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 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.

This work addresses the problem of adaptive control for stochastic linear quadratic regulators (LQR) with time-varying chance constraints. The authors propose a safe, optimism-based exploration method formulated via semidefinite programming (SDP), which selects optimistic policies while progressively retracting to verifiably safe ones, thereby satisfying safety constraints at every step while achieving low regret. The key innovation lies in establishing, for the first time in constrained LQR settings, a regret bound of $\tilde{O}(\sqrt{T})$, improving upon the prior best-known rate of $\tilde{O}(T^{2/3})$. The approach handles unbounded process noise through chance constraints and introduces a novel analytical framework based on system covariance—replacing conventional cost-function-based analyses—to theoretically guarantee both safety and near-optimal performance.

This work addresses the challenge of online linear quadratic regulator (LQR) control for unknown dynamical systems under communication constraints. Conventional approaches suffer from persistent noise due to per-step state quantization and high communication overhead. To overcome these limitations, the authors propose a novel paradigm wherein the local agent estimates system dynamics from observations and transmits only this dynamic estimate over a low-rate communication link to a remote controller. The remote controller then computes the optimal policy and sends it back for execution using the local agent’s exact state. The study establishes, for the first time, an Ω(log T) fundamental lower bound on communication complexity required to achieve sublinear regret and introduces the QCE-LQR algorithm that matches this bound. As the quantization resolution increases, QCE-LQR’s regret smoothly converges to that of the unquantized certainty-equivalent benchmark. Empirical evaluations on four standard systems, including a Boeing 747 model, demonstrate that QCE-LQR attains performance comparable to the unquantized controller within T = 10,000 steps.

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.

本文解决了iLQR算法在处理约束时的数值稳定性问题，通过引入基于Gauss-Newton结构的平方根方法，利用QR分解简化了反馈增益和Cholesky因子的计算。

This work addresses the challenge of infeasible quadratic programs (QPs) in robotic systems—arising from conflicting objectives, modeling errors, or degenerate contacts—which commonly cause numerical failure in existing differentiable QP solvers that assume feasibility. To overcome this, we propose Elastic ODYN, a primal-dual non-interior-point QP solver based on a smooth ℓ₂ elastic relaxation that converges to the closest feasible solution when constraints are unsatisfiable and recovers physically consistent dual variables via lightweight refinement. Our method enables, for the first time, stable differentiable optimization over infeasible QPs, supports warm-starting, and robustly handles degenerate scenarios. We introduce the differentiable Elastic OdynLayer and an infeasibility-aware sequential quadratic programming (SQP) framework, Elastic OdynSQP. Experiments on standard QPs, singular contacts, parameter identification, and trajectory optimization for quadrupedal and humanoid robots demonstrate significant improvements over prior approaches in robustness, warm-start performance, and convergence reliability.