A Nonlinear Model Predictive Control Method for Trajectory Planning of UAV Swarms

A Zeroing Neural Dynamics-Based Predictive Control Algorithm for Manipulator Trajectory Tracking and Obstacle Avoidance

To address the problem of robotic manipulator trajectory tracking in complex environments subject to obstacle constraints and multilevel joint constraints, this paper proposes a trajectory tracking and obstacle avoidance control method based on model predictive control (MPC) and zeroing neural dynamics (ZND). First, a unified optimization model is established by simultaneously considering trajectory tracking error, control input smoothness, obstacle avoidance requirements, and multilevel joint constraints, so as to achieve safe motion control of the manipulator in complex environments. Then, for the resulting time-varying optimization problem, a corresponding ZND-based online solver is designed to dynamically update the optimization variables in real time, thereby improving the computational efficiency of MPC and satisfying the real-time requirement of the control system. The proposed method enables the endeffector to accurately track the desired trajectory while effectively avoiding collisions with obstacles and satisfying multilevel joint constraints. Simulation results demonstrate that the proposed method achieves favorable performance in terms of tracking accuracy, obstacle avoidance safety, and online computational efficiency.

Model Predictive Path Integral for Agile UAV Control with Online Collision Avoidance

Trajectory Planning for Unmanned Surface Vehicles in Complex Environments via CasADi-Based Optimal Control

Results indicate that the proposed formulation can generate safe, feasible, and smooth USV trajectories in representative complex environments.

Trajectory Tracking Control of Autonomous Mobile Robots via Linearized Model Predictive Control: Theory and Simulation Validation

Accurate trajectory tracking is a fundamental requirement for autonomous mobile robots (AMRs) operating in complex environments. This paper addresses the tracking control problem for AMRs subject to kinematic constraints. A linearized model predictive control (LMPC) framework is proposed to effectively reduce trajectory tracking errors while ensuring smooth control inputs and high computational efficiency. First, the nonlinear kinematic model of the robot is derived and linearized around the reference trajectory using Taylor series expansion to obtain a discrete-time linear error dynamic model. Second, the tracking problem is formulated as a constrained finite-horizon optimization problem, which is transformed into a standard quadratic programming (QP) form to guarantee computational efficiency. Extensive simulations are conducted using a complex butterfly-shaped trajectory characterized by continuous curvature variations. The results demonstrate that the proposed controller achieves high tracking accuracy with centimeter-level position errors and generates feasible control inputs that strictly satisfy constraints, thereby demonstrating the robustness and effectiveness of the proposed controller.

Reinforcement learning-guided multi-objective trajectory planning for obstacle avoidance in robotic manipulators

Robotic manipulators operating in cluttered environments require collision-free trajectories that remain executable under kinematic and dynamic constraints. This paper proposes a reinforcement learning (RL)-guided multi-objective trajectory planning framework, termed RL-MOP-HNE, for a 6-DOF UR5 manipulator. The planning model simultaneously minimizes path length, energy consumption, and execution time while satisfying collision-avoidance, kinematic, and dynamic constraints. A tabular SARSA agent is embedded into the evolutionary search to adaptively select search behaviours according to the current optimization state. To improve the balance between exploration and exploitation, a Gaussian-perturbation adaptive hybrid crossover operator is integrated with a hierarchical neighborhood evolution (HNE) strategy, enabling progressive population refinement throughout the search process. The proposed method is evaluated in three representative environments with increasing planning complexity, including single-obstacle, narrow three-obstacle, and irregular five-obstacle scenarios, and is compared with MOEA/D, MOPSO, MSCLPSO, NSGA-II, and RL-NSGA-II. Experimental results show that RL-MOP-HNE generates feasible trajectories in all test cases and achieves the lowest dynamic-stability-prioritized composite scores among the compared algorithms. The planned trajectories exhibit smoother joint motion and lower velocity fluctuations, although these improvements are generally accompanied by longer execution times. Complementary analyses, including time scaling, manipulability, clearance evaluation, statistical significance tests, and ablation studies, further explain the performance characteristics of the proposed framework and quantify the contribution of its key components. The proposed framework is therefore well suited to robotic applications where motion stability and dynamic executability are of greater importance than minimum-time operation.

Trajectory planning of unmanned aerial vehicles in uncertain environments based on model predictive control and dual-model control

Aiming at the difficulties of autonomous trajectory planning for unmanned aerial vehicles (UAVs) in unknown and dynamically uncertain environments, such as insufficient prediction ability, easy falling into local optimum, poor environmental adaptability, and information scarcity caused by passive obstacle avoidance, traditional single-model predictive control is difficult to balance computational efficiency and uncertainty compensation. Therefore, this paper proposes a UAV trajectory planning method based on Model Predictive Control dual-model cooperative control, which organically integrates model predictive control with the exploration-exploitation strategy. The method adopts a dual architecture of nominal model + online learning model: the simplified nominal model ensures real-time solution efficiency, and the online learning model dynamically compensates for unmodeled dynamics and environmental disturbances. By introducing information gain and uncertainty attenuation indicators into the MPC optimization objective, the UAV is guided to actively explore unknown areas, avoid local optimum traps, and achieve a dynamic balance between exploration and exploitation. Simulation verification based on MATLAB and CasAdi toolbox shows that the proposed method can significantly reduce environmental uncertainty, improve trajectory tracking accuracy and active obstacle avoidance ability, and exhibit stronger robustness, decision-making intelligence and flight efficiency in complex unstructured environments.