Robot Trajectory Tracking

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Overview

Robot trajectory tracking studies how a robot can follow a desired path or time-varying motion, which is essential for tasks such as manipulation, navigation, flight, and locomotion. Common approaches include feedback control such as PID, backstepping, and sliding-mode methods; model-predictive control; and adaptive, learning-based, and iterative-learning controllers that compensate for uncertain dynamics or repeated errors. Work spans mobile robots, aerial vehicles, manipulators, soft robots, and humanoids, with attention to sensing, actuator limits, collision avoidance, and real-time computation. A central challenge is balancing precise tracking with robustness and safety when models, terrain, payloads, contact, or reference motions change.

Latest papers

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137 papers17 papers in the last four weeks, down 15% on the four weeks before. 0.1% of all new papers.

Mar 13, 2026

PhyGile: Physics-Prefix Guided Motion Generation for Agile General Humanoid Motion Tracking

Humanoid robots are expected to execute agile and expressive whole-body motions in real-world settings. Existing text-to-motion generation models are predominantly trained on captured human motion datasets, whose priors assume human biomechanics, actuation, mass distribution, and contact strategies. When such motions are directly retargeted to humanoid robots, the resulting trajectories may satisfy geometric constraints (e.g., joint limits and pose continuity) and appear kinematically reasonable. However, they frequently violate the physical feasibility required for real-world execution. To address these issues, we present PhyGile, a unified framework that closes the loop between robot-native motion generation and General Motion Tracking (GMT). PhyGile performs physics-prefix-guided robot-native motion generation at inference time, directly generating robot-native motions in a 262-dimensional skeletal space with physics-guided prefixes, thereby eliminating inference-time retargeting artifacts and reducing generation-execution discrepancies. Before physics-prefix adaptation, we train the GMT controller with a curriculum-based mixture-of-experts scheme, followed by post-training on unlabeled motion data to improve robustness over large-scale robot motions. During physics-prefix adaptation, the GMT controller is further fine-tuned with generated objectives under physics-derived prefixes, enabling agile and stable execution of complex motions on real robots. Extensive offline and real-robot experiments demonstrate that PhyGile expands the frontier of text-driven humanoid control, enabling stable tracking of agile, highly difficult whole-body motions that go well beyond walking and low-dynamic motions typically achieved by prior methods.

Jiacheng Bao, Haoran Yang, Yucheng Xin +7

Northwestern Polytechnical University · Shanghai AI Laboratory · University of Science and Technology of China +4

Robot Trajectory TrackingHumanoid Robot ControlRobot Motion GenerationHumanoid Motion Tracking
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Mar 10, 2026

Hierarchical Task Model Predictive Control for Sequential Mobile Manipulation Tasks

Mobile manipulators are envisioned to serve more complex roles in people's everyday lives. With recent breakthroughs in large language models, task planners have become better at translating human verbal instructions into a sequence of tasks. However, there is still a need for a decision-making algorithm that can seamlessly interface with the high-level task planner to carry out the sequence of tasks efficiently. In this work, building on the idea of nonlinear lexicographic optimization, we propose a novel Hierarchical-Task Model Predictive Control framework that is able to complete sequential tasks with improved performance and reactivity by effectively leveraging the robot's redundancy. Compared to the state-of-the-art task-prioritized inverse kinematic control method, our approach has improved hierarchical trajectory tracking performance by 42% on average when facing task changes, robot singularity and reference variations. Compared to a typical single-task architecture, our proposed hierarchical task control architecture enables the robot to traverse a shorter path in task space and achieves an execution time 2.3 times faster when executing a sequence of delivery tasks. We demonstrated the results with real-world experiments on a 9 degrees of freedom mobile manipulator.

Xintong Du, Siqi Zhou, Angela P. Schoellig

Learning Systems and Robotics Lab (www.learnsyslab.org) at the Technical University of Munich, Germany, and the University of Toronto Institute for Aerospace Studies, Canada · University of Toronto Robotics Institute · Munich Institute of Robotics and Machine Intelligence (MIRMI) +1

Hierarchical Robot ControlMobile ManipulationModel Predictive ControlRobot Trajectory Tracking
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Mar 9, 2026

Trajectory Tracking Control Design for Autonomous Helicopters with Guaranteed Error Bounds

This paper presents a systematic framework for computing formally guaranteed trajectory tracking error bounds for autonomous helicopters based on Robust Positive Invariant (RPI) sets. The approach establishes a closed-loop translational error dynamics which is cast into polytopic linear parameter-varying form with bounded additive and state-dependent disturbances. Ellipsoidal RPI sets are computed, yielding explicit position error bounds suitable as certified buffer zones in upper-level trajectory planning. Three controller architectures are compared with respect to the conservatism of their error bounds and tracking performance. Simulation results on a nonlinear helicopter model demonstrate that all architectures satisfy the derived bounds, while highlighting trade-offs between performance and the conservatism of the computed invariant set.

Philipp Schitz, Johann C. Dauer, Paolo Mercorelli

Institute of Flight Systems, German Aerospace Center (DLR), 38108 Braunschweig, Germany · Institute for Production Technology and Systems, Leuphana University of Lueneburg, 21335 Lueneburg, Germany

Robot Trajectory TrackingAerial RoboticsRobust Control
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Mar 5, 2026

Control Lyapunov Functions for Underactuated Soft Robots

Soft and soft-rigid hybrid robots are inherently underactuated and operate under tight actuator limits, making task-space control with stability guarantees challenging. Common nonlinear strategies for soft robots (e.g., those based on PD control) often rely on the assumption of full actuation with no actuator limits. This paper presents a general control framework for task-space regulation and tracking of underactuated soft robots under bounded inputs. The method enforces a rapidly exponentially stabilizing control Lyapunov function as a convex inequality constraint while simultaneously satisfying underactuated full-body dynamics and actuator bounds. We validate the approach in simulation on several platforms spanning increasing underactuation: a simple two link tendon-driven "finger", a trimmed helicoid manipulator, and a highly underactuated spiral robot. We compare against a number of baseline methods from the literature. Results show improved task-space accuracy and consistent Lyapunov convergence under input limits, achieving superior set-point and trajectory-tracking performance.

Huy Pham, Zach J. Patterson

Mechanical and Aerospace Engineering, Case Western Reserve University

Robotic ControlSoft RoboticsLyapunov-Based ControlRobot Trajectory Tracking
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Mar 5, 2026

Residual RL-MPC for Robust Microrobotic Cell Pushing Under Time-Varying Flow

Contact-rich micromanipulation in microfluidic flow is challenging because small disturbances can break pushing contact and induce large lateral drift. We study planar cell pushing with a magnetic rolling microrobot that tracks a waypoint-sampled reference curve under time-varying Poiseuille flow in simulation. We propose a hybrid controller that augments a nominal MPC with a learned residual policy trained by SAC. The policy outputs a bounded 2D velocity correction that is contact-gated, so residual actions are applied only during robot-cell contact, preserving reliable approach behavior and stabilizing learning. All methods share the same actuation interface and speed envelope for fair comparisons. Simulation results show improved robustness and tracking accuracy over pure MPC and PID under nonstationary flow, with generalization from a clover training curve to unseen circle and square trajectories. A residual-bound sweep identifies an intermediate correction limit as the best trade-off, which we use in all benchmarks.

Yanda Yang, Sambeeta Das

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716, USA

Robot Trajectory TrackingContact-Rich Robotic ManipulationRobust ControlModel Predictive ControlRobotic ManipulationResidual Policy Learning
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Mar 5, 2026

Accelerating Sampling-Based Control via Learned Linear Koopman Dynamics

This paper presents an efficient model predictive path integral (MPPI) control framework for systems with complex nonlinear dynamics. To improve the computational efficiency of classic MPPI while preserving control performance, we replace the nonlinear dynamics used for trajectory propagation with a learned linear deep Koopman operator (DKO) model, enabling faster rollout and more efficient trajectory sampling. The DKO dynamics are learned directly from interaction data, eliminating the need for analytical system models. The resulting controller, termed MPPI-DK, is evaluated in simulation on pendulum balancing and surface vehicle navigation tasks, and validated on hardware through reference-tracking experiments on a quadruped robot. Experimental results demonstrate that MPPI-DK achieves control performance close to MPPI with true dynamics while substantially reducing computational cost, enabling efficient real-time control on robotic platforms.

Wenjian Hao, Yuxuan Fang, Zehui Lu +1

independent researcher

Robotic ControlRobot Trajectory TrackingMPPI ControlOptimal Control
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Feb 21, 2026

Learning to Localize Reference Trajectories in Image-Space for Visual Navigation

We present LoTIS, a model for visual navigation that provides robot-agnostic image-space guidance by localizing a reference RGB trajectory in the robot's current view, without requiring camera calibration, poses, or robot-specific training. Instead of predicting actions tied to specific robots, we predict the image-space coordinates of the reference trajectory as they would appear in the robot's current view. This creates robot-agnostic visual guidance that easily integrates with local planning. Consequently, our model's predictions provide guidance zero-shot across diverse embodiments. By decoupling perception from action and learning to localize trajectory points rather than imitate behavioral priors, we enable a cross-trajectory training strategy for robustness to viewpoint and camera changes. We outperform state-of-the-art methods by 20-50 percentage points in success rate on conventional forward navigation, achieving 94-98% success rate across diverse sim and real environments. Furthermore, we achieve over 5x improvements on challenging tasks where baselines fail, such as backward traversal. The system is straightforward to use: we show how even a video from a phone camera directly enables different robots to navigate to any point on the trajectory. Videos, demo, and code are available at https://finnbusch.com/lotis.

Finn Lukas Busch, Matti Vahs, Quantao Yang +4

Division of Robotics, Perception, and Learning, KTH Royal Institute of Technology, Sweden, and also affiliated with Digital Futures

Robot Trajectory TrackingRobot NavigationVision-Based Robot ControlCross-Embodiment TransferVisual Robot Navigation
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Feb 20, 2026

Quasi-Periodic Gaussian Process Predictive Iterative Learning Control

Repetitive motion tasks are common in robotics, but performance can degrade over time due to environmental changes and robot wear and tear. Iterative learning control (ILC) improves performance by using information from previous iterations to compensate for expected errors in future iterations. This work incorporates the use of Quasi-Periodic Gaussian Processes (QPGPs) into a predictive ILC framework to model and forecast disturbances and drift across iterations. Using a recent structural equation formulation of QPGPs, the proposed approach enables efficient inference with complexity O(p3)\mathcal{O}(p^3) instead of O(i2p3)\mathcal{O}(i^2p^3), where pp denotes the number of points within an iteration and ii represents the total number of iterations, specially for larger ii. This formulation also enables parameter estimation without loss of information, making continual GP learning computationally feasible within the control loop. By predicting next-iteration error profiles rather than relying only on past errors, the controller achieves faster convergence and maintains this under time-varying disturbances. We benchmark the method against both standard ILC and conventional Gaussian Process (GP)-based predictive ILC on three tasks, autonomous vehicle trajectory tracking, a three-link robotic manipulator, and a real-world Stretch robot experiment. Across all cases, the proposed approach converges faster and remains robust under injected and natural disturbances while reducing computational cost. This highlights its practicality across a range of repetitive dynamical systems.

Unnati Nigam, Radhendushka Srivastava, Faezeh Marzbanrad +1

IITB-Monash Research Academy, IIT Bombay, Mumbai, India · Department of Mathematics, IIT Bombay, Mumbai, India · Department of Electrical and Computer Systems Engineering, Monash University, Clayton, Melbourne, Australia

Iterative Learning ControlRobotic ControlGaussian ProcessesAdaptive ControlGaussian Process RegressionRobot Trajectory Tracking
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Feb 17, 2026

Lyapunov-Based PI-Like Control for Robust Trajectory Tracking of a Four-Wheel Independently Driven and Steered Robot: Design and Experimental Validation

In this paper, a Lyapunov-based synthesis of a PI-like controller is proposed for robust trajectory tracking of an independently driven and steered four-wheel mobile robot. For the robot considered in this work, an explicit structurally verified mathematical model is used to enable systematic controller design with rigorous stability guarantees suitable for real time implementation. An augmented Lyapunov-based practical stability analysis is developed for the combined velocity-error and integral-error dynamics of the inner loop, yielding explicit bounds and sufficient conditions for practical stability and uniform ultimate boundedness of the combined velocity-error and integral-error state. The resulting control law retains a PI-like structure with model-based feedforward compensation, making it suitable for implementation on standard embedded platforms while improving robustness against configuration dependent residual dynamics and unmodelled effects. The effectiveness and robustness of the proposed design are demonstrated experimentally on a four-wheel independently steered and independently driven mobile robot platform, under both horizontal and vertical operating conditions and benchmarked against a PI controller and a sliding-mode controller.

Branimir Ćaran, Vladimir Milić, Marko Švaco +1

Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb HR-10000, Croatia · Croatian Academy of Sciences and Arts, Zagreb 10000, Croatia

PID ControlRobot Trajectory TrackingFeedback ControlMobile RoboticsRobust ControlLyapunov-Based Control
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Feb 17, 2026

A Comparison of Bayesian Prediction Techniques for Mobile Robot Trajectory Tracking

This paper presents a performance comparison of different estimation and prediction techniques applied to the problem of tracking multiple robots. The main performance criteria are the magnitude of the estimation or prediction error, the computational effort and the robustness of each method to non-Gaussian noise. Among the different techniques compared are the well known Kalman filters and their different variants (e.g. extended and unscented), and the more recent techniques relying on Sequential Monte Carlo Sampling methods, such as particle filters and Gaussian Mixture Sigma Point Particle Filter.

Jose Luis Peralta-Cabezas, Miguel Torres-Torriti, Marcelo Guarini-Hermann

Dept. of Electrical Engineering, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Casilla 306-22, Santiago, Chile

Robot Trajectory TrackingRobot State EstimationBayesian FilteringParticle FilteringKalman FilteringMulti-Robot Systems
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Feb 2, 2026

Tilt-Ropter: A Fully Actuated Hybrid Aerial-Terrestrial Vehicle with Tilt Rotors and Passive Wheels

In this work, we present Tilt-Ropter, a fully actuated hybrid aerial-terrestrial vehicle (HATV) that integrates tilt rotors with passive wheels to enable efficient multi-modal locomotion. Unlike conventional underactuated HATVs, the fully actuated design of Tilt-Ropter allows decoupled force and torque control, improving maneuverability and ground locomotion efficiency. A unified nonlinear model predictive controller (NMPC) is developed to track reference trajectories, enforce non-holonomic constraints, and accommodate contact effects across locomotion modes, while ensuring actuator feasibility through dedicated control allocation. To address complex wheel-ground dynamics, an external wrench estimator is incorporated to provide real-time interaction wrench estimates. The system is validated through simulation and real-world experiments, including seamless air-ground transitions and trajectory tracking tasks. Experimental results demonstrate low tracking errors in both modes and reveal a 92.8% reduction in power consumption during ground locomotion compared with flight, highlighting the platform's potential for long-duration missions where energy efficiency is critical.

Ruoyu Wang, Xuchen Liu, Zongzhou Wu +3

Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong · Faculty of Engineering, The University of Hong Kong, Pokfulam, Hong Kong · Peng Cheng Laboratory, Shenzhen, Guangdong, China

Robotic ControlRobot Trajectory TrackingAerial RoboticsRobotics
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Jan 21, 2026

DWPP: Dynamic Window Pure Pursuit Considering Velocity and Acceleration Constraints

Pure pursuit and its variants are widely used for mobile robot path tracking owing to their simplicity and computational efficiency. However, many conventional approaches do not explicitly account for velocity and acceleration constraints, resulting in discrepancies between commanded and actual velocities that result in overshoot and degraded tracking performance. To address this problem, this paper proposes dynamic window pure pursuit (DWPP), which fundamentally reformulates the command velocity computation process to explicitly incorporate velocity and acceleration constraints. Specifically, DWPP formulates command velocity computation in the velocity space (the vv-ωω plane) and selects the command velocity as the point within the dynamic window that is closest to the line ω=κvω= κv. Experimental results demonstrate that DWPP avoids constraint-violating commands and achieves superior path-tracking accuracy compared with conventional pure pursuit methods. The proposed method has been integrated into the official Nav2 repository and is publicly available (https://github.com/ros-navigation/navigation2).

Fumiya Ohnishi, Masaki Takahashi

Robot Trajectory Tracking
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Jan 13, 2026

Simplifying ROS2 controllers with a modular architecture for robot-agnostic reference generation

This paper introduces a novel modular architecture for ROS2 that decouples the logic required to acquire, validate, and interpolate references from the control laws that track them. The design includes a dedicated component, named Reference Generator, that receives references, in the form of either single points or trajectories, from external nodes (e.g., planners), and writes single-point references at the controller's sampling period via the existing ros2_control chaining mechanism to downstream controllers. This separation removes duplicated reference-handling code from controllers and improves reusability across robot platforms. We implement two reference generators: one for handling joint-space references and one for Cartesian references, along with a set of new controllers (PD with gravity compensation, Cartesian pose, and admittance controllers) and validate the approach on simulated and real Universal Robots and Franka Emika manipulators. Results show that (i) references are tracked reliably in all tested scenarios, (ii) reference generators reduce duplicated reference-handling code across chained controllers to favor the construction and reuse of complex controller pipelines, and (iii) controller implementations remain focused only on control laws.

Davide Risi, Vincenzo Petrone, Antonio Langella +3

Department of Information Engineering, Electrical Engineering and Applied Mathematics (DIEM), University of Salerno, 84084 Fisciano, Italy

Robotic ControlRobot Trajectory Tracking
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Dec 13, 2025

Temporal Cascading of Planning and Control for Quadrotor MPC

Many aerial tasks involving quadrotors demand both instant reactivity and long-horizon planning for obstacle avoidance, energy efficiency, or trajectory tracking. High-fidelity models enable accurate control but are too slow for long horizons. Low-fidelity planners scale but cannot directly control the system, necessitating cascaded architectures. Prevailing hierarchical approaches plan with a simplified model and use a high-fidelity controller for tracking, yet this decomposition is inherently suboptimal. The controller is limited by the coarse plan, and conventional MPC alternatives shorten the horizon to stay real-time feasible. We present UNIQUE, an MPC architecture that replaces this hierarchical stacking with temporal cascading. The planning problem is formulated as the second-tail horizon of a single multi-phase MPC, rather than being solved separately. We align costs across horizons, derive feasibility constraints for the point-mass planning model, and introduce transition constraints that convert high-fidelity states into meaningful low-fidelity states. Parallel point-mass and mixed-integer solvers address nonconvexities while incorporating progressive 3D obstacle smoothing over the planning horizon. In simulations and real flights, under equal computational budgets, UNIQUE improves closed-loop tracking by up to 75% compared with standard MPC and hierarchical baselines. Ablations and Pareto analyses confirm performance gains across variations in horizon, constraint approximations, and smoothing schedules.

Rudolf Reiter, Chao Qin, Leonard Bauersfeld +1

Robotics and Perception Group, Department of Informatics, University of Zurich, Andreasstrasse 15, 8050 Zurich, Switzerland · Institute for Aerospace Studies, University of Toronto, 4925 Dufferin Street, Toronto, ON M3H 5T6, Canada

Robot Trajectory TrackingAerial RoboticsModel Predictive ControlUAV Trajectory OptimizationQuadrotor ControlSafe Motion Planning
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Jun 10, 2025

Differentiable Physics-Informed Adaptive Koopman Control for Stable Flight under Unknown Disturbances

Uncertainties and disturbances in robotic systems, such as aerodynamic forces, are fundamentally outcomes of physical interactions with the environment, manifesting as learnable spatiotemporal sequences rather than random noise. However, achieving high-precision control for robotic systems operating in unstructured environments is often hindered by complex unmodeled dynamics and external disturbances. While learning-based methods offer powerful approximation capabilities, they typically suffer from heavy reliance on offline training and lack theoretical guarantees. Conversely, traditional robust control strategies are predominantly reactive, limited to instantaneous estimation without the foresight to anticipate future disturbance trends. To bridge this gap, this paper proposes a differentiable data-enabled Koopman control framework termed DEKC. Unlike black-box approaches, DEKC adopts a hybrid modeling strategy that retains the nominal physics model while employing a deep neural network to parameterize the lifting function of Koopman operator for unknown residual dynamics. Crucially, the framework formulates disturbances as a dynamical system, learning their temporal evolution in a global linear space. This enables the prediction of future disturbance trajectories, which are explicitly integrated into controller for preemptive compensation. Furthermore, an online backward gradient update mechanism is introduced to ensure real-time adaptation to time-varying uncertainties. Numerical simulations on a tethered space robot demonstrate the efficacy of the proposed DEKC in mitigating highly coupled uncertainties. Complementing these results, real-world experiments on a quadrotor substantiate its superiority in tracking agile trajectories under uncertainties induced by aerodynamics and suspended payload.

Ao Jin, Qiujin Liang, Tao Zhang +2

Research Center for Intelligent Robotics, School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China · Department of Automation, Tsinghua University, Beijing 100080, China

Robot Trajectory TrackingRobust ControlFeedback ControlQuadrotor ControlDisturbance RejectionAdaptive Control
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Jun 5, 2025

A Three-Stage Offline SDRE-Based Control Framework for Human Motion Reproduction on a Suspended Bipedal Robot

This paper presents a three-stage offline command generation framework for reproducing human lower-limb motion on a suspended bipedal robot while matching torque trajectories computed from the robot dynamic model. First, State-Dependent Riccati Equation (SDRE) control derives the reference torque trajectory for the measured motion. Second, parameterized optimization converts this trajectory into trapezoidal joint velocity commands under motor speed and acceleration limits. Third, a proportional-integral-derivative linear quadratic regulator (PID-LQR) compensation scheme refines these commands using experimental tracking data. The platform executes the resulting profiles to reproduce human walking and squatting motions recorded by a Vicon system, allowing evaluation of tracking accuracy and repeatability. Results show that the average root mean square error (RMSE) and standard deviation (STD) of joint angles across repeated trials remain below 7° and 0.33°, respectively. Joint angle and torque trajectory comparisons show lower maximum RMSE and STD values than those for MPC and IPSO-PID in every reported case. The framework enables accurate and repeatable motion reproduction within actuator limits, providing controlled and measurable conditions that can reduce reliance on human participation and associated risks during preliminary evaluation of devices for assistive walking, gait training, and rehabilitation.

Ping-Kong Huang, Chien-Wu Lan, Chin-Tien Wu +1

Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan · Department of Electrical Engineering, National Central University, Taoyuan City 320317, Taiwan

Robotic ControlRobot Trajectory TrackingHuman-to-Robot Motion ImitationRobot Motion GenerationFeedback Control
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Mar 18, 2025

Learning-Based Progressive Barrier Control for Robot Manipulators with Initial Errors Outside Prescribed Tracking Bounds

Robot manipulators may start a new task with a tracking error larger than the prescribed tolerance. Conventional barrier controllers generally require the initial error to lie within this tolerance, which prevents their direct use under such conditions. This paper develops a progressive barrier controller that gradually contracts an initial error bound to the required value within a prescribed time. The robot can therefore start outside the final bound, while the direct joint-position error satisfies it after the transition. The closed-form control law combines progressive barrier feedback with an online adaptive torque term based on an actor--critic structure. A Lyapunov analysis establishes bounded closed-loop signals and gives sufficient conditions for satisfaction of the final tracking bound. Two-link simulations consider large initial errors, actuator saturation, dynamic variations, disturbances, and measurement errors. The adaptive term reduces the median root-mean-square tracking error by 45.1% compared with the zero-weight progressive barrier controller. The simulations also map the initial errors that can be handled at different transition times under fixed torque limits. Finally, an experiment on a Niryo Ned3 Pro illustrates tracking performance using measured position and motor-current data.

Hamed Rahimi Nohooji, Danial Zafaranchizadeh Moghaddam, Abolfazl Zaraki +1

Automation and Robotics Research Group, Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, 1855 Luxembourg, Luxembourg · School of Physics, Engineering and Computer Science (SPECS), and Robotics Research Group of the University of Hertfordshire, Hatfield, AL10 9AB, United Kingdom

Robotic ControlRobot Trajectory TrackingFeedback ControlAdaptive Control
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