pd controller tuning

To address the need for adaptive and robust control in dynamic environments for autonomous micro-drones pursuing multiple objectives—energy efficiency, high-precision localization, and high-speed navigation—this paper proposes AirPilot: an interpretable deep reinforcement learning (DRL)-enhanced nonlinear PID controller based on Proximal Policy Optimization (PPO). Methodologically, AirPilot integrates DRL with classical PID control via a novel deep fusion architecture enabling online, automatic parameter tuning. It is trained in Gazebo simulation and deployed end-to-end on real hardware—the COEX Clover micro-drone—using ROS/PX4 hardware-in-the-loop integration. Key contributions include the first deep architectural integration of DRL and PID for online adaptation, and the first real-world validation of such a hybrid controller on a resource-constrained micro-UAV. Experimental results demonstrate that AirPilot reduces navigation error by 90% compared to the default PX4 PID, while improving effective navigation speed by 21%, reducing settling time by 17%, and decreasing overshoot by 16% relative to manually tuned PID.

This study addresses the challenge of achieving high-performance control in active magnetic levitation systems when an accurate mathematical model is unavailable. The authors propose and compare two data-driven optimal differential feedback control strategies: a direct model-free reinforcement learning approach and an indirect method based on system identification. An innovative “epoch-loop” policy iteration mechanism is introduced to enhance exploration diversity through multiple rounds of data collection, effectively mitigating bias issues inherent in model-free learning. Experimental results demonstrate that both approaches outperform a nominal model-based controller. Notably, the direct model-free method—enabled by multi-epoch data collection—exhibits significantly superior stability and control performance compared to the indirect approach, which relies on a single batch of data combined with Dynamic Mode Decomposition with control (DMDc) and Prediction Error Method (PEM) for system identification.

This paper addresses adaptive tracking control for Euler–Lagrange systems subject to strict state, input, and time (SIT) constraints. We propose a model-free, smooth, and prescribed-time convergent control strategy. Methodologically, we introduce a novel approximation-free framework that integrates time-varying barrier functions with smooth time-base generating functions—eliminating the need for neural network or fuzzy approximators. Our contributions are threefold: (1) the first control architecture unifying time-varying barrier functions and smooth time-base generation without function approximation; (2) explicit characterization of the coupling constraints among admissible control authority, disturbance rejection capability, and the initial feasible domain; and (3) incorporation of time-varying filtered error constraints and saturated control actions to guarantee strict, persistent satisfaction of all SIT constraints. Rigorous analysis proves that tracking errors converge within any user-prescribed time to an arbitrarily small residual set. Experiments on three robotic manipulators demonstrate superior convergence accuracy, constraint adherence, and robustness compared to state-of-the-art methods.

This study addresses the challenge of improving path-tracking accuracy and lap time in autonomous racing by effectively predicting inverse lateral vehicle dynamics to minimize steering corrections from the feedback controller. The authors propose a novel empirical feedforward method—Empirical Handling Dynamics (EHD)—based on polynomial surface fitting, which captures speed-dependent nonlinear steering characteristics with minimal parametrization. Using a high-fidelity two-track vehicle dynamics simulator, they systematically evaluate two learning-based and two empirical feedforward controllers within a combined open-loop and closed-loop validation framework. Results show that although learning-based approaches achieve the lowest open-loop prediction error, the proposed EHD method delivers superior closed-loop robustness and faster lap times, underscoring the critical importance of evaluating feedforward strategies within the full control stack rather than in isolation.

To address the challenge of aerial manipulators failing to satisfy end-effector tracking performance constraints within a prescribed time, this paper proposes a novel time-sequenced control framework integrating prescribed performance control (PPC) with quadratic programming (QP). Methodologically: (1) A user-tunable prescribed performance function is introduced to rigorously bound both the convergence time and steady-state error of tracking; (2) A task-driven reference command allocation mechanism enables coordinated motion optimization between the quadrotor base and the Delta manipulator; (3) A physically constrained QP formulation ensures actuation safety and feasibility. Experimental results demonstrate that the method achieves high-precision end-effector positioning within the specified time horizon, with tracking errors strictly confined within the prescribed performance envelope throughout execution. This significantly enhances the system’s time determinism and robustness against disturbances and model uncertainties.

This study addresses performance degradation in discrete-time PID control of robotic joints, commonly caused by actuator saturation, sampling delays, and measurement noise. To tackle these practical constraints, the authors propose a tuning method that integrates the Jury stability criterion, an anti-windup mechanism, and a safety-constrained Bayesian optimization framework within a zero-order hold discretization model. The approach optimizes controller gains with respect to the Integral Absolute Error (IAE) while incorporating behavioral safety certification to pre-eliminate infeasible parameter candidates, thereby significantly improving sample efficiency. Simulation results under uncertain conditions demonstrate that the median IAE is reduced from 0.843 to 0.430, overshoot remains below 2%, and 11.6% of unsafe gain configurations are effectively excluded during the optimization process.

This work addresses the challenge of verifying closed-loop safety in safety-critical systems—such as aerospace applications—where neural network controllers act as black boxes. The authors propose a sampling-free reachability analysis framework that embeds a trained neural network into the system dynamics to form an autonomous closed-loop system. By integrating high-order Taylor expansions, automated domain partitioning, and polynomial bounding techniques, the method rigorously confines the propagation of state uncertainties over event manifolds. This approach enables, for the first time, a global, sound, and efficient reachability analysis of neural network-controlled systems, yielding tight upper and lower bounds on controller outputs across large state spaces. These guaranteed bounds facilitate reliable safety certification and informed mission-level decision-making.

This work addresses the lack of stability guarantees in data-driven velocity control for nonlinear robotic systems by proposing a virtual reference feedback tuning (VRFT) method augmented with passivity constraints. Requiring only three minutes of exploratory data, the approach designs an implicit finite impulse response (iFIR) controller that achieves stable velocity tracking in both joint and Cartesian spaces. Experimental validation on a Franka Emika Panda robot demonstrates up to a 74.5% reduction in Cartesian velocity tracking error. In contrast to conventional learning-based controllers, the proposed framework uniquely combines data-driven learning capability with theoretical closed-loop stability guarantees. Furthermore, it enables rapid relearning following dynamic changes, overcoming a key limitation of existing methods that struggle to simultaneously ensure high performance and stability.

In dynamically uncertain environments, conventional control methods suffer degraded performance, while existing data-driven approaches often struggle with low sample efficiency and lack of stability guarantees. This work proposes the L-Learning framework, which uniquely integrates Lyapunov stability theory with Lagrangian mechanics to explicitly learn a system’s energy function from data, thereby embedding closed-loop stability assurance directly into the learning process. By leveraging this principled approach, the method achieves significantly improved trajectory tracking accuracy while substantially reducing sample complexity—all without compromising theoretical stability. Consequently, L-Learning unifies high sample efficiency, strong stability guarantees, and superior tracking performance, making it well-suited for real-world robotic control applications.

This work addresses the low sample efficiency and discontinuous control inputs of traditional Model Predictive Path Integral (MPPI) control in high-dimensional settings, as well as the limited adaptability of fixed-gain PID controllers in complex path-tracking tasks. The authors propose an MPPI–PID framework that performs sampling-based optimization not in the high-dimensional control sequence space, but in the low-dimensional space of PID gains—a novel approach that significantly improves sample efficiency and yields smoother control signals. Integrating residual learning for dynamics modeling with real-time gain adaptation, the method achieves tracking performance comparable to conventional MPPI using drastically fewer samples in a miniature forklift path-following experiment, while substantially reducing control effort compared to fixed-gain PID. A theoretical analysis further unifies MPPI and MPPI–PID from an information-theoretic perspective, clarifying how dimensionality affects both sample efficiency and input continuity.