6-DOF Control Research Articles

Accurate Raycasting Selection With Rotation Gesture Using a 6-DOF Tracking Device.

A six degrees of freedom (6-DOF) controller is a commonly used input device in three-dimensional user interface (3DUI) applications. However, for the fundamental task of target selection in 3D space, the selection accuracy decreases owing to the Heisenberg effect during the manipulation of the 6-DOF controller. Based on the pointing action of a 6-DOF device, we establish the mathematical model for raycasting and analyze the possibility of using a rotation gesture to select a target. This study proposes a target selection method using the axial rotation of the user's wrist, which reduces the negative impact of a discrete input for triggering the selection on accuracy. The detection model can identify the start time of the user's rotation action. The custom designed control display gain (CD gain) function can maintain the ray's stability during the rotation gesture. This method was verified using a 6-DOF pen and Vive controller in three experiments. The results show that the accuracy of the proposed rotation gesture-based raycasting target selection method is superior to that of the traditional button-pressing method, and it can be integrated into existing tracking systems for further application.

RetroSphere: Enabling Low-power and Affordable 3D Input for Lightweight Augmented Reality Devices

RetroSphere introduces a self-contained 6-degree-of-freedom (6DoF) controller tracker, designed for seamless integration with resourceconstrained Augmented Reality (AR) devices such as AR glasses and smartphones. This system employs a tracking mechanism using one to three retro-reflective spheres on a passive controller, thus eliminating the need for any onboard electronics or batteries. Detection is enabled by a stereo pair of mass-produced infrared blob trackers, each outfitted with infrared LED emitters. The system utilizes a lightweight stereo depth-estimation algorithm on an Arduino-compatible ESP32 microcontroller to achieve 6DoF tracking. RetroSphere achieves a tracking accuracy of approximately 96.5%, with positional errors as low as 3.5 cm across a tracking range of 100 cm, while maintaining a power consumption of just about 400 mW. The complete hardware and firmware details for RetroSphere are available as open source on GitHub: https://github.com/AnantaBalaji/RetroSphere

6-DOF UAV Path planning and tracking control for obstacle avoidance: a deep learning-based integrated approach

Path planning is crucial for achieving autonomous and safe flight of fixed-wing unmanned aerial vehicles (UAVs). The existing methods generally cannot simultaneously balance real-time performance, near optimality, and feasibility in three-dimensional obstacle environments. To this end, this paper proposes a deep learning-based integrated path planning and tracking control framework for obstacle avoidance. First, a fundamental framework, including an interfered fluid dynamical system (IFDS)-based path planning module and a backstepping control-based path tracking module, is established. Then, to satisfy high real-time requirements, a long short-term memory (LSTM)-based fast online decision-making network matched with the IFDS is developed. Extensive training samples are generated by the fundamental framework, and receding horizon control is employed to optimize these samples so that the LSTM can provide near-optimal coefficients for the IFDS. Furthermore, the dynamic characteristics of an actual UAV system and the performance of the tracking controller are fully considered during sample generation, enabling that the paths planned by the LSTM-assisted IFDS are highly feasible. Finally, the results of numerical simulations and hardware-in-the-loop experiments show that our method can plan near-optimal obstacle-free paths with high feasibility in real-time.

A six degrees-of-freedom cable-driven robotic platform for head-neck movement.

This paper introduces a novel cable-driven robotic platform that enables six degrees-of-freedom (DoF) natural head-neck movements. Poor postural control of the head-neck can be a debilitating symptom of neurological disorders such as amyotrophic lateral sclerosis and cerebral palsy. Current treatments using static neck collars are inadequate, and there is a need to develop new devices to empower movements and facilitate physical rehabilitation of the head-neck. State-of-the-art neck exoskeletons using lower DoF mechanisms with rigid linkages are limited by their hard motion constraints imposed on head-neck movements. By contrast, the cable-driven robot presented in this paper does not constrain motion and enables wide-range, 6-DoF control of the head-neck. We present the mechatronic design, validation, and control implementations of this robot, as well as a human experiment to demonstrate a potential use case of this versatile robot for rehabilitation. Participants were engaged in a target reaching task while the robot applied both assistive and resistive moments on the head during the task. Our results show that neck muscle activation increased by 19% when moving the head against resistance and decreased by 28-43% when assisted by the robot. Overall, these results provide a scientific justification for further research in enabling movement and identifying personalized rehabilitation for motor training. Beyond rehabilitation, other applications such as applying force perturbations on the head to study sensory integration and applying traction to achieve pain relief may benefit from the innovation of this robotic platform which is capable of applying controlled 6-DoF forces/moments on the head.

Coupled translation and attitude tracking control for multi-satellite electromagnetic formation flight based on dual quaternion

Electromagnetic formation flight technology utilizes electromagnetic force and torque between satellites to control satellites’ relative position and attitude without consuming propellant, thus having broad application prospects. However, the dynamics of electromagnetic formation flying are nonlinear and strongly coupled, posing challenges to the 6-DOF control of electromagnetic formation and the magnetic dipole allocation of satellites. The frequency division multiplexing method can approximate decoupling formation dynamics by loading multi-frequency AC carriers onto satellite magnetic dipoles and is likely to achieve more control functions. A design method for AC carriers based on frequency division multiplexing is proposed to decouple formation dynamics while controlling electromagnetic force and torque. This paper further provides an analytical solution for the magnetic dipoles of the electromagnetic force/torque equations. In addition, in response to external disturbances, model uncertainty, and the inability to obtain relative velocity and angular velocity information of the formation system, this paper establishes a 6-DOF coupling model based on dual quaternion and implements tracking control using the active disturbance rejection control method. Based on the internal force characteristics of the electromagnetic formation, an expression for the equilibrium distribution of reaction wheel torque is derived to avoid some reaction wheels’ rapid accumulation of angular momentum. Numerical simulation results show the effectiveness of the proposed control method.

Passivity-based fractionated payload 6-DOF maneuver control using electromagnetic actuation

Employing fractionated spacecraft architecture with electromagnetic actuation into space missions can enhance resilience and flexibility since all subsystems of conventional monolithic spacecraft are separated as several modules to be easily replaced on-orbit when failure happens. Previous electromagnetic configuration used in fractionated spacecraft would render unexpected forces and torques which may undermine the stability of entire system. This paper considers the maneuver of a separated payload in a fractionated spacecraft architecture (FSA) using electromagnetic actuation with adaptive passivity-based control. The FSA consists of a fractionated payload module (FPM) and a supporting spacecraft module (SSM). Relative motion dynamics of FPM and SSM are formulated on SE(3). An adaptive passivity-based 6-DOF motion control scheme is established for FPM's translation and rotation tracking control simultaneously. The closed-loop equilibrium can be attained by the proposed passivity-based 6-DOF control scheme. The controller has no requirement for the precise inertia knowledge of FPM, which processes the robustness of the modelling errors. Numerical simulations are presented to show the effectiveness of the proposed control scheme.

Fixed-time anti-saturation control with concise system structure for the 6-DOF motion of spacecraft

Abstract This paper proposes a fixed-time anti-saturation (FT-AS) control scheme with a simple control loop for the 6-Degree-of-Freedom tracking (6-DOF) control problem of spacecraft with parameter uncertainties, external disturbances and input saturation. Considering the external disturbance and parameter uncertainties, the dynamical model of the tracking error is established. The traditional methods of handling input saturation usually add anti-saturation subsystems in the control system to suppress the impact of input overshoot. However, this paper directly inputs the input overshoot into the tracking error model, thus constructing a modified lumped disturbance term that includes the influence of input overshoot. Then, a novel fixed-time disturbance observer (FT-DO) is designed to estimate and compensate for this modified lumped disturbance. Therefore, there is no need to add the anti-saturation structures in the control loop, significantly reducing the complexity of the system. Finally, an observer-based fixed-time non-singular terminal sliding mode (FT-NTSM) controller is designed to guarantee the fixed-time stability of the whole system. In this way, the convergence time of the proposed scheme does not depend on the system’s initial conditions. Simulation results illustrate that the proposed method keeps the control input within the limit while achieving high-precision tracking control of attitude and position.

Hybrid Visual-Ranging Servoing for Positioning Based on Image and Measurement Features.

In this article, a hybrid visual-ranging servoing method is proposed to realize high-precision positioning tasks with a 6-degree of freedom (DOF) manipulator. This method utilizes the image and measurement features directly in the control loop. Without the need of complex image feature design and attitude estimation, this method realizes the 6-DOF control of a robot. A vital challenge in traditional vision-based systems is avoiding local minima and singularity problems. To tackle this issue, a full-rank interaction matrix hybrid visual servo (FRHVS) design criterion is proposed, which guarantees that the hybrid interaction matrix and its pseudoinverse matrix are both full rank. Moreover, the interaction matrix for these hybrid strategies, which combines image features with other sensors features, is derived in an analytical form. Experiments on a 6-DOF manipulator show that the proposed method is effective and has global asymptotic stability and high precision.

Test mass 6-DOF control allocation based on the null space for space gravitational wave mission

This paper proposes a novel 6-DOF control allocation based on the null space for the capture control of the drag-free spacecraft's test mass. Considering the unconstrained case firstly, an unconstrained time-varying weighted least square control allocation method is presented to eliminate the error of the test mass along every DOF synchronously to reach stable state quickly. Subsequently, an improved null-space-based method is proposed to modify the unconstrained solution of the weighted least square control allocation to meet the physical constraints of actuators. Numerical simulations illustrate the efficiency of the proposed control allocation scheme, which realizes coordinated control allocation of 6-DOF generalized forces, reduces allocation errors and computational complexity, and improves the efficiency of capture control of the test mass.

Control of Electromagnetic Formation Flight of Two Satellites in Low Earth Orbits

Electromagnetic formation flight uses the electromagnetic interaction between satellites to provide maneuver control for formation satellites, with the advantages of no propellant consumption, long life, and high flexibility. However, high-precision control for electromagnetic formation flight is challenging because of the nonlinear and coupling characteristics of the dynamics, optimal assignment of magnetic dipoles, model uncertainties, and the angular momentum management issues caused by the geomagnetic field. This paper studies the 6-DOF control problem of two-satellite electromagnetic formation flight in low-Earth orbit. A new electromagnetic frame is introduced to promote the decoupling of the translation dynamics model and the electromagnetic model. The electromagnetic model can be expressed as a simple two-dimensional model in this electromagnetic frame. The proposed electromagnetic force envelope diagram can intuitively show the relationship between electromagnetic force and magnetic dipoles, providing practical guidance for dipole assignment. The frequency division multiplexing method is designed for angular momentum management considering the effect of the earth’s magnetic field on the electromagnetic satellites, and the active disturbance rejection control method is used to solve the 6-DOF stability problem with external disturbance and model uncertainties. Numerical simulation verifies the effectiveness of the proposed control method and angular momentum management strategy.

Velocity-free finite-time relative 6-DOF control for rigid spacecraft

This paper addresses the problem of spacecraft’s finite-time six-degree-of-freedom(6-DOF) tracking control without velocity measurements. To estimate the unavailable incorporating angular and translational velocities (called the dual angular velocity), a novel observer with a simple structure and finite-time stability is presented in the dual quaternion frame. Then, combining with the estimated dual angular velocity, a continuous velocity-free 6-DOF control law based on the terminal sliding mode theory is presented to achieve the relative pose tracking objective within finite time, where the specially designed parameter ensures its non-singularity. In addition, by designing the desired reference frame, the proposed control law can be employed to various missions. With consideration of the observation errors, a rigorous proof is provided to demonstrate the finite-time stability of the observer-alone and the observer-based control law. Two typical numerical simulations, hovering and circumnavigation, are carried out to verify the effectiveness of the proposed method.

A Study on the Control Method of 6-DOF Magnetic Levitation System Using Non-Contact Position Sensors

Recently, due to the development of semiconductor technology, high-performance memory and digital convergence technology that integrates and implements various functions into one semiconductor chip has been regarded as the next-generation core technology. In the semiconductor manufacturing process, various motors are being applied for automated processes and high product reliability. However, dust and shaft loss due to mechanical friction of a general motor system composed of motor-bearing are problematic for semiconductor wafer processing. In addition, in the edge bread remove (EBR) process after the photoresist application process, a nozzle position control system for removing unnecessary portions of the wafer edge is absolutely necessary. Therefore, in this paper, in order to solve the problems occurring in the semiconductor process, a six-degrees-of-freedom (6-DOF) magnetic levitation system without shaft and bearing was designed for application to the semiconductor process system; and an integrated driving control algorithm for 6-DOF control (levitation, rotation, tilt (Roll-Pitch), X-Y axis movement) using the force of each current component derived through current vector control was proposed. Finally, the 6-DOF magnetic levitation system with the non-contact position sensors was fabricated and the validity of the 6-DOF magnetic levitation control method proposed in this paper was verified through a performance test using a prototype.

Partial State Feedback MRAC Based Reconfigurable Fault-Tolerant Control of Drag-Free Satellite With Bounded Estimation Error

Aiming at the ultra-precision and ultra-stable requirements of drag-free control in space detection missions, a multivariable model reference adaptive control (MRAC) scheme is proposed in this paper based on partial observation state, to provide adaptive suppression of uncertain disturbances and improve detection accuracy. The MRAC scheme utilizes model output matching with partial state containing uniform and bounded observation error, and estimates the unknown state parameters through the adaptive law and high-frequency gain decomposition. In response to the actuator bias fault of the drag-free satellite, a set of state error iterative convergence sequence in the actuator loop is established based on the sequence Lyapunov analysis, which is further introduced into the reconfiguration control input to achieve the fault-tolerant target without changing the nominal controller. Through the Lyapunov stability analysis, the convergence of the closed-loop system states in the presence of actuator faults and observation errors is obtained. Numerical simulation results for a 6-DOF drag-free control system demonstrate the effectiveness of the proposed MRAC-based reconfigurable fault-tolerant control scheme.

RetroSphere

Advanced AR/VR headsets often have a dedicated depth sensor or multiple cameras, high processing power, and a high-capacity battery to track hands or controllers. However, these approaches are not compatible with the small form factor and limited thermal capacity of lightweight AR devices. In this paper, we present RetroSphere, a self-contained 6 degree of freedom (6DoF) controller tracker that can be integrated with almost any device. RetroSphere tracks a passive controller with just 3 retroreflective spheres using a stereo pair of mass-produced infrared blob trackers, each with its own infrared LED emitters. As the sphere is completely passive, no electronics or recharging is required. Each object tracking camera provides a tiny Arduino-compatible ESP32 microcontroller with the 2D position of the spheres. A lightweight stereo depth estimation algorithm that runs on the ESP32 performs 6DoF tracking of the passive controller. Also, RetroSphere provides an auto-calibration procedure to calibrate the stereo IR tracker setup. Our work builds upon Johnny Lee's Wii remote hacks and aims to enable a community of researchers, designers, and makers to use 3D input in their projects with affordable off-the-shelf components. RetroSphere achieves a tracking accuracy of about 96.5% with errors as low as ~3.5 cm over a 100 cm tracking range, validated with ground truth 3D data obtained using a LIDAR camera while consuming around 400 mW. We provide implementation details, evaluate the accuracy of our system, and demonstrate example applications, such as mobile AR drawing, 3D measurement, etc. with our Retrosphere-enabled AR glass prototype.

Finite-Time Prescribed Performance Control for Space Circumnavigation Mission With Input Constraints and Measurement Uncertainties

This article presents a 6-DOF attitude-orbit synchronous control problem for the space circumnavigation (SCN) mission with parameter uncertainties, time-varying uncertainties, and input constraints. In particular, from the perspective of engineering application, time-varying measurement uncertainties are taken into account of the 6-DOF attitude–orbit coupling kinematics and dynamics, and the analytical solution of the desired attitude is derived based on the measured relative orbit information with measurement uncertainties. To drive the active spacecraft approach to the faulty target safely, a time-varying exponential prescribed convergence boundary is introduced into the sliding surface. A finite-time disturbance observer is involved in equivalent tracking errors for compensating the mismatched uncertainties. In addition, an auxiliary system is designed to overcome the instability danger caused by input constraints. The stability of the controlled system is discussed in the nonautonomous finite-time stable framework, which is proved via Lyapunov analysis that the attitude-orbit tracking errors converge to the equilibrium within finite time. The simulation experiment with mismatched uncertainties and prescribed constraints shows the superiority of the designed control scheme.

A SLAM-based 6DoF controller with smooth auto-calibration for virtual reality

A SLAM-based 6DoF controller with smooth auto-calibration for virtual reality

Twistor-Based Adaptive Pose Control of Spacecraft for Landing on an Asteroid With Collision Avoidance

In the framework of twistors, a saturated adaptive six-degree-of-freedom (6-DOF) control law for asteroid landing, which avoids the collision between the spacecraft and asteroid, is proposed with both the inertial parameters of the spacecraft and the bounds of the uncertainties unknown. First, the 6-DOF dynamics of the spacecraft relative to the desired coordinate frame is represented in a unified way by the application of twistors, and the collision avoidance constraint is established via separating the spacecraft and asteroid with an elaborately designed safety surface. Then, a saturated controller for the landing is proposed with the collision avoidance constraint considered by combining the backstepping method and artificial potential field technique. Further, the inertial parameters and the upper bounds of the magnitude of the uncertainties in the controller are substituted with their estimates obtained from the designed adaptive laws. Finally, the previous design is adjusted slightly to complete the adaptive control scheme. The stability of the closed-loop system is proven via Lyapunov theory, and numerical simulations are presented to demonstrate the effectiveness of the control scheme. The proposed adaptive control law can fully consider the orbit-attitude coupling and effectively enforce the collision avoidance constraint in the presence of unknowns in asteroid landing missions.

Distributed Control of 6-DOF Leader-Following Multi-Spacecraft Formation near an Asteroid Based on Scaled Twistors

This paper addresses the distributed six-degree-of-freedom (6-DOF) control problem of translation-rotation coupled spacecraft formation in the vicinity of an asteroid. Due to the complicated gravity field of an asteroid, there exist no circular or elliptic orbits for the spacecraft, which renders the control schemes designed for the spacecraft formation near the Earth inapplicable. In the framework of twistors, a distributed leader-following control scheme is proposed by combining the dynamic surface technique and consensus theory under an undirected communication topology. First, a scaled-twistor-based position-attitude coupled dynamic model of the spacecraft near an asteroid is established to circumvent numerical difficulty. Since the state of the leader can only be accessed by a subset of the followers, an observer is integrated into the control scheme to estimate the state of the leader for each follower. Then, the pose error between each follower and its desired pose is represented by the scaled twistor. Based on the error dynamics, virtual control is designed according to the consensus theory, and a distributed control law is proposed via the dynamic surface method. To eliminate the large control effort and aggressive transient in the initial phase, adaptive gains are introduced into the control scheme. Furthermore, neural networks (NNs) are used to compensate for not only the external disturbances but also the filter errors resulting from the dynamic surface method. By virtue of the Lyapunov theory, it is proved that the pose errors of the followers are ensured to converge to the neighborhood of the origin, and all the adaptive gains and weights of the NNs are bounded. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.

Learning-Based 6-DOF Control for Autonomous Proximity Operations Under Motion Constraints

This article proposes areinforcement learning (RL)-based six-degree-of-freedom (6-DOF) control scheme for the final-phase proximity operations of spacecraft. The main novelty of the proposed method are from two aspects: 1) The closed-loop performance can be improved in real-time through the RL technique, achieving an online approximate optimal control subject to the full 6-DOF nonlinear dynamics of spacecraft; 2) nontrivial motion constraints of proximity operations are considered and strictly obeyed during the whole control process. As a stepping stone, the dual-quaternion formalism is employed to characterize the 6-DOF dynamics model and motion constraints. Then, an RL-based control scheme is developed under the dual-quaternion algebraic framework to approximate the optimal control solution subject to a cost function and a Hamilton–Jacobi–Bellman equation. In addition, a specially designed barrier function is embedded in the reward function to avoid motion constraint violations. The Lyapunov-based stability analysis guarantees the ultimate boundedness of state errors and the weight of NN estimation errors. Besides, we also show that a PD-like controller under dual-quaternion formulation can be employed as the initial control policy to trigger the online learning process. The boundedness of it is proved by a special Lyapunov strictification method. Simulation results of prototypical spacecraft missions with proximity operations are provided to illustrate the effectiveness of the proposed method.

Artificial potential function based spacecraft proximity maneuver 6-DOF control under multiple pyramid-type constraints

This paper addresses the problem of spacecraft six degree of freedom (6-DOF) pose tracking control with collision avoidance and field of view (FOV) pyramid-type constraints during the autonomous proximity maneuver. The constraints are modeled as pyramid envelopes, which can better represent some real cases with less conservativeness comparing with commonly used cone-shaped model. A novel modeling method is proposed to describe the pyramid-type constraints in the dual-quaternion frame. Based on the specific geometric property of the pyramid constraints, a new convex artificial potential function (APF) with only one global minimum is designed, which incorporates the pose constraints into the control design procedure. Then, an integrated APF based control law is presented to simultaneously control the rotational and translational motion of the spacecraft without violating the pyramid constraints. The stability of the closed-loop system is demonstrated through the Lyapunov theory, and numerical simulation results are carried out to show the effectiveness of the proposed control law.