Trajectory tracking for microswimmers remains a key challenge in microrobotics, where low-Reynolds-number dynamics make control design particularly complex. In this work, we formulate the trajectory tracking problem as an optimal control problem and solve it using a combination of B-spline parametrization with Bayesian optimization, allowing the treatment of high computational costs without requiring complex gradient computations. Applied to a flagellated magnetic swimmer, the proposed method reproduces a variety of target trajectories, including biologically inspired paths observed in experimental studies. We further evaluate the approach on a three-sphere swimmer model, demonstrating that it can adapt to and partially compensate for wall-induced hydrodynamic effects. The proposed optimization strategy can be applied consistently across models of different fidelity, from low-dimensional ODE-based models to high-fidelity PDE-based simulations, showing its robustness and generality. These results highlight the potential of Bayesian optimization as a versatile tool for optimal control strategies in microscale locomotion under complex fluid-structure interactions.
Motion planning for autonomous vehicles requires spatio-temporal motion plans (i.e. state trajectories) to account for dynamic obstacles. This requires a trajectory tracking control process which faithfully tracks planned trajectories. In this paper, a control scheme is presented which first optimizes a planned trajectory and then tracks the optimized trajectory using a feedback-feedforward controller. The feedforward element is calculated in a model predictive manner with a cost function focusing on driving performance. Stability of the error dynamic is then guaranteed by the design of the fe…
Precise trajectory tracking is a crucial property for \acp{MAV} to operate in cluttered environment or under disturbances. In this paper we present a detailed comparison between two state-of-the-art model-based control techniques for \ac{MAV} trajectory tracking. A classical \ac{LMPC} is presented and compared against a more advanced \ac{NMPC} that considers the full system model. In a careful analysis we show the advantages and disadvantages of the two implementations in terms of speed and tracking performance. This is achieved by evaluating hovering performance, step response, and aggressive…
Optimal point-to-point trajectory planning for planar redundant manipulator is considered in this study. The main objective is to minimize the sum of the position error of the end-effector at each intermediate point along the trajectory so that the end-effector can track the prescribed trajectory accurately. An algorithm combining Genetic Algorithm and Pattern Search as a Generalized Pattern Search GPS is introduced to design the optimal trajectory. To verify the proposed algorithm, simulations for a 3-D-O-F planar manipulator with different end-effector trajectories have been carried out. A c…
Unmapped areas and aerodynamic disturbances render autonomous navigation with quadrotors extremely challenging. To fly safely and efficiently, trajectory planners and trackers must be able to navigate unknown environments with unpredictable aerodynamic effects in real-time. When encountering aerodynamic effects such as strong winds, most current approaches to quadrotor trajectory planning and tracking will not attempt to deviate from a determined plan, even if it is risky, in the hope that any aerodynamic disturbances can be resisted by a robust controller. This paper presents a novel systemat…
Zhejiang University（浙江大学）；Huzhou Institute, Zhejiang University（浙江大学湖州研究院）
This paper proposes Elastic Tracker, a flexible trajectory planning framework that can deal with challenging tracking tasks with guaranteed safety and visibility. Firstly, an object detection and intension-free motion prediction method is designed. Then an occlusion-aware path finding method is proposed to provide a proper topology. A smart safe flight corridor generation strategy is designed with the guiding path. An analytical occlusion cost is evaluated. Finally, an effective trajectory optimization approach enables to generate a spatio-temporal optimal trajectory within the resultant fligh…
Norwegian University of Science and Technology（挪威科技大学）；SINTEF DIGITAL（SINTEF数字研究所）
In this article we show how the model predictive path following controller allows robotic manipulators to stop at obstructions in a way that model predictive trajectory tracking controllers cannot. We present both controllers as applied to robotic manipulators, simulations for a two-link manipulator using an interior point solver, consider discretization of the optimal control problem using collocation or Runge-Kutta, and discuss the real-time viability of our implementation of the model predictive path following controller.
Zhejiang University（浙江大学）；Huzhou Institute of Zhejiang University（浙江大学湖州研究院）
The visibility of targets determines performance and even success rate of various applications, such as active slam, exploration, and target tracking. Therefore, it is crucial to take the visibility of targets into explicit account in trajectory planning. In this paper, we propose a general metric for target visibility, considering observation distance and angle as well as occlusion effect. We formulate this metric into a differentiable visibility cost function, with which spatial trajectory and yaw can be jointly optimized. Furthermore, this visibility-aware trajectory optimization handles dy…
The goal of this paper is to develop a continuous optimization-based refinement of the reference trajectory to 'push it out' of the obstacle-occupied space in the global phase for Multi-rotor Aerial Vehicles in unknown environments. Our proposed approach comprises two planners: a global planner and a local planner. The global planner refines the initial reference trajectory when the trajectory goes either through an obstacle or near an obstacle and lets the local planner calculate a near-optimal control policy. The global planner comprises two convex programming approaches: the first one helps…
National Institute of Informatics（国立信息学研究所）；Hunan University（湖南大学）
In the path planning problem of autonomous application, the existing studies separately consider the path planning and trajectory tracking control of the autonomous vehicle and few of them have integrated the trajectory planning and trajectory control together. To fill in this research gap, this study proposes an integrated trajectory planning and trajectory control method. This paper also studies the collision avoidance problem of autonomous by considering static and dynamic obstacles. Simulation results have been presented to show the effectiveness of the proposed control method.
Zhejiang University（浙江大学）；Huzhou Institute of Zhejiang University（浙江大学湖州研究院）
Unmanned surface vessels (USVs) are widely used in ocean exploration and environmental protection fields. To ensure that USV can successfully perform its mission, trajectory planning and motion tracking are the two most critical technologies. In this paper, we propose a novel trajectory generation and tracking method for USV based on optimization theory. Specifically, the USV dynamic model is described with differential flatness, so that the trajectory can be generated by dynamic RRT* in a linear invariant system expression form under the objective of optimal boundary value. To reduce the samp…
DMVC-Tracker: Distributed Multi-Agent Trajectory Planning for Target Tracking Using Dynamic Buffered Voronoi and Inter-Visibility Cells
Artificial Intelligence Institute of Seoul National University（首尔国立大学人工智能研究院）；Seoul National University of Science and Technology（首尔科学技术大学）；Seoul National University（首尔国立大学）
Massachusetts Institute of Technology（麻省理工学院）；Imperial College London（帝国理工学院）；University of Washington（华盛顿大学）
Accurate and agile trajectory tracking in sub-gram Micro Aerial Vehicles (MAVs) is challenging, as the small scale of the robot induces large model uncertainties, demanding robust feedback controllers, while the fast dynamics and computational constraints prevent the deployment of computationally expensive strategies. In this work, we present an approach for agile and computationally efficient trajectory tracking on the MIT SoftFly, a sub-gram MAV (0.7 grams). Our strategy employs a cascaded control scheme, where an adaptive attitude controller is combined with a neural network policy trained …
Trajectory Tracking Control Design for Autonomous Helicopters with Guaranteed Error Bounds
Institute of Flight Systems, German Aerospace Center (DLR)（飞行系统研究所，德国航天中心）；Institute for Production Technology and Systems, Leuphana University of Lueneburg（生产技术与系统研究所，路比哈大学）
Harbin Institute of Technology Shenzhen（哈尔滨工业大学深圳校区）
To promote the widespread use of mobile robots in diverse fields, the performance of trajectory tracking must be ensured. To address the constraints and nonlinear features associated with mobile robot systems, we apply nonlinear model predictive control (MPC) to realize the trajectory tracking of mobile robots. Specifically, to alleviate the online computational complexity of nonlinear MPC, this paper devises a lattice piecewise affine (PWA) approximation method that can approximate both the nonlinear system and control law of explicit nonlinear MPC. The kinematic model of the mobile robot is …
QP Chaser: Polynomial Trajectory Generation for Autonomous Aerial Tracking
Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）；Department of Mechanical System Design Engineering, Seoul National University of Science and Technology（首尔科学技术大学机械系统设计工程系）；Department of Aerospace Engineering, Seoul National University（首尔国立大学航空航天工程系）；Samsung Research, Samsung Electronics（三星电子三星研究）
University of Leuven (KU Leuven)（鲁汶大学）；Nanyang Technological University（南洋理工大学）
More efficient agricultural machinery is needed as agricultural areas become more limited and energy and labor costs increase. To increase their efficiency, trajectory tracking problem of an autonomous tractor, as an agricultural production machine, has been investigated in this study. As a widely used model-based approach, model predictive control is preferred in this paper to control the yaw dynamics of the tractor which can deal with the constraints on the states and the actuators in a system. The yaw dynamics is identified by using nonlinear least squares frequency domain system identifica…
The demonstrations of micro-robotic systems in minimally invasive medicine include an individual or a swarm of microswimmer of various origin, artificial or biohybrid, often with an external computer-controlled electromagnetic field. There are several in vivo and in vitro control performances with artificial microswimmers but control of a bio-hybrid microswimmer using an open kinematic chain remains untouched. In this work, non-contact maneuvering control of a single magnetotactic bacterium cell is simulated. The results show that the proposed system is capable of adjusting the heading of the …
Georgia Institute of Technology（佐治亚理工学院）；Meta Reality Lab（Meta现实实验室）
This paper describes a stereo image-based visual servoing system for trajectory tracking by a non-holonomic robot without externally derived pose information nor a known visual map of the environment. It is called trajectory servoing. The critical component is a feature-based, indirect Simultaneous Localization And Mapping (SLAM) method to provide a pool of available features with estimated depth, so that they may be propagated forward in time to generate image feature trajectories for visual servoing. Short and long distance experiments show the benefits of trajectory servoing for navigating …
Enforcing safety on precise trajectory tracking is critical for aerial robotics subject to wind disturbances. In this paper, we present a learning-based safety-preserving cascaded quadratic programming control (SPQC) for safe trajectory tracking under wind disturbances. The SPQC controller consists of a position-level controller and an attitude-level controller. Gaussian Processes (GPs) are utilized to estimate the uncertainties caused by wind disturbances, and then a nominal Lyapunov-based cascaded quadratic program (QP) controller is designed to track the reference trajectory. To avoid unexp…
Delft University of Technology（代尔夫特理工大学）；University of Leuven (KU Leuven)（鲁汶大学）
This paper proposes a new robust trajectory tracking error-based control approach for unmanned ground vehicles. A trajectory tracking error-based model is used to design a linear model predictive controller and its control action is combined with feedforward and robust control actions. The experimental results show that the proposed control structure is capable to let a tractor-trailer system track both linear and curvilinear target trajectories with low tracking error.
This paper presents a control method and trajectory planner for vehicles with first-order nonholonomic constraints that guarantee asymptotic convergence to a time-indexed trajectory. To overcome the nonholonomic constraint, a fixed point in front of the vehicle can be controlled to track a desired trajectory, albeit with a steady-state error. To eliminate steady state error, a sufficiently smooth trajectory is reformulated for the new reference point such that, when tracking the new trajectory, the vehicle asymptotically converges to the original trajectory. The resulting zero-error tracking l…
University of Toronto Institute for Aerospace Studies（多伦多大学航空航天研究所）；Cairo University（开罗大学）
Transfer learning has the potential to reduce the burden of data collection and to decrease the unavoidable risks of the training phase. In this letter, we introduce a multirobot, multitask transfer learning framework that allows a system to complete a task by learning from a few demonstrations of another task executed on another system. We focus on the trajectory tracking problem where each trajectory represents a different task, since many robotic tasks can be described as a trajectory tracking problem. The proposed multirobot transfer learning framework is based on a combined $\mathcal{L}_1…
Two-layer adaptive trajectory tracking controller for quadruped robots on slippery terrains
Institute of Computer Science, Foundation for Research and Technology–Hellas（希腊基础研究与技术基金会计算机科学研究所）；Hellenic Mediterranean University（希腊地中海大学）；University of Crete（克里特大学）
Flexible-joint manipulators are governed by complex nonlinear dynamics, defining a challenging control problem. In this work, we propose an approach to learn an outer-loop joint trajectory tracking controller with deep reinforcement learning. The controller represented by a stochastic policy is learned in under two hours directly on the real robot. This is achieved through bounded reference correction actions and use of a model-free off-policy learning method. In addition, an informed policy initialization is proposed, where the agent is pre-trained in a learned simulation. We test our approac…
We study a trajectory tracking problem for a multi-rotor in the presence of modeling error and external disturbances. The desired trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume that only position and orientation measurements for the multi-rotor and position measurements for the reference system can be accessed. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the feed-forward term required for trajectory tracking, the multi-rotor states, as well as modeling error and external disturbances. We design…
Heteroscedastic Bayesian Optimization-Based Dynamic PID Tuning for Accurate and Robust UAV Trajectory Tracking
College of Computer Science, Chongqing University（重庆大学计算机学院）；School of Computing, Macquarie University（麦考瑞大学计算机学院）；School of Automation, Chongqing University（重庆大学自动化学院）
Safe mobility for unmanned ground vehicles requires reliable detection of other vehicles, along with precise estimates of their locations and trajectories. Here we describe the algorithms and system we have developed for accurate trajectory estimation of nearby vehicles using an onboard scanning LADAR. We introduce a variable-axis Ackerman steering model and compare this to an independent steering model. Then for robust tracking we propose a multi-hypothesis tracker that combines these kinematic models to leverage the strengths of each. When trajectories estimated with our techniques are input…
Continuous trajectory tracking control of quadrotors is complicated when considering noise from the environment. Due to the difficulty in modeling the environmental dynamics, tracking methodologies based on conventional control theory, such as model predictive control, have limitations on tracking accuracy and response time. We propose a Time-attenuating Twin Delayed DDPG, a model-free algorithm that is robust to noise, to better handle the trajectory tracking task. A deep reinforcement learning framework is constructed, where a time decay strategy is designed to avoid trapping into local opti…
This paper proposes a systematic solution that uses an unmanned aerial vehicle (UAV) to aggressively and safely track an agile target. The solution properly handles the challenging situations where the intent of the target and the dense environments are unknown to the UAV. Our work is divided into two parts: target motion prediction and tracking trajectory planning. The target motion prediction method utilizes target observations to reliably predict the future motion of the target considering dynamic constraints. The tracking trajectory planner follows the traditional hierarchical workflow.A t…
Laboratoire des Sciences du Numérique de Nantes（南特数字科学实验室）；CNRS（法国国家科学研究中心）；IRT Jules Verne（儒勒·凡尔纳研究院）；Inria（法国国家信息与自动化研究所）；Univ Rennes（雷恩大学）；IRISA（雷恩信息与自动化系统研究所）
Cable-Driven Parallel Robots (CDPRs) are a kind of parallel robots that have cables instead of rigid links. Implementing vision-based control on CDPRs leads to a good final accuracy despite modeling errors and other perturbations in the system. However, unlike final accuracy, the trajectory to the goal can be affected by the perturbations in the system. This paper proposes the use of trajectory tracking to improve the robustness of 2 1/2 D visual servoing control of CDPRs. Lyapunov stability analysis is performed and, as a result, a novel workspace, named control stability workspace, is define…
Collision Risk Quantification and Conflict Resolution in Trajectory Tracking for Acceleration-Actuated Multi-Robot Systems
Harbin Institute of Technology Shenzhen（哈尔滨工业大学（深圳））；Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies（广东省新型安全智能技术重点实验室）；Southern University of Science and Technology（南方科技大学）；University of Oulu（奥卢大学）
Trajectory Tracking for UAVs: An Interpolating Control Approach
New Technologies for the Information Society Research Center（信息技术新技术研究中心）；Department of Cybernetics（控制论系）；Faculty of Applied Sciences（应用科学学院）；University of West Bohemia（西波希米亚大学）
Human trajectory prediction has received increased attention lately due to its importance in applications such as autonomous vehicles and indoor robots. However, most existing methods make predictions based on human-labeled trajectories and ignore the errors and noises in detection and tracking. In this paper, we study the problem of human trajectory forecasting in raw videos, and show that the prediction accuracy can be severely affected by various types of tracking errors. Accordingly, we propose a simple yet effective strategy to correct the tracking failures by enforcing prediction consist…
Accuracy and stability are common requirements for Quadrotor trajectory tracking systems. Designing an accurate and stable tracking controller remains challenging, particularly in unknown and dynamic environments with complex aerodynamic disturbances. We propose a Quantile-approximation-based Distributional-reinforced Uncertainty Estimator (QuaDUE) to accurately identify the effects of aerodynamic disturbances, i.e., the uncertainties between the true and estimated Control Contraction Metrics (CCMs). Taking inspiration from contraction theory and integrating the QuaDUE for uncertainties, our n…
