This paper presents a static and dynamic torque analysis of the CABLESSail concept, which involves cables routed along the length of the flexible booms that hold the solar sail membrane in such a manner that tensioning the cables results in a bending deformation of the booms. This provides a mechanism where actuation of the cables can be used to create an imbalance in solar radiation pressure (SRP) on the sail and thus, impart SRP torques that can be used for momentum management of the solar sail. Simulation results are included that demonstrate how large SRP torques can be induced by tensioning the solar sail's cables, which can be used for momentum management. Comparisons to the existing active mass translator technology are included, along with simulations demonstrating the ability to reliably generate control torques in the presence of an uncertain sail membrane shape. An appendix contains a detailed derivation of the cable-actuated solar sail dynamic model used in this work.

This paper introduces a cable-length-based extended Kalman filter (L-EKF) framework to estimate the end-effector pose of a cable-driven parallel robot (CDPR). The L-EKF fuses end-effector accelerometer and rate gyroscope measurements with cable-length measurements. The main contribution compared to prior CDPR pose estimation EKF methods is that the L-EKF framework does not require an iterative forward kinematics algorithm to be solved each time step, reducing the computation time of the EKF. Moreover, the L-EKF is amenable to the inclusion of colored measurement noise, which provides a more realistic quantification of the kinematic uncertainty present in the cable-length measurements. Experimental results demonstrate that the L-EKF is computationally more efficient than previous forward-kinematics-based EKF methods, as well as the moderate improvement in pose estimation provided by the colored noise model.

This paper presents an estimation and control framework that enables the targeted reentry of a drag-modulated spacecraft in the presence of atmospheric density uncertainty. In particular, an extended Kalman filter is used to estimate errors between the in-flight atmospheric density and the atmospheric density used to generate the guidance trajectory. This information is leveraged within a model predictive control strategy to improve tracking performance, reduce control effort, and increase robustness to actuator saturation compared to the state-of-the-art approach. The estimation and control framework is tested in a Monte Carlo simulation campaign with historical space weather data. These simulation efforts demonstrate that the proposed framework is able to stay within 100 km of the guidance trajectory at all points in time for 98.4% of cases. The remaining 1.6% of cases were pushed away from the guidance by large density errors, many due to significant solar storms and flares, that could not physically be compensated for by the drag control device. For the successful cases, the proposed framework was able to guide the deorbiting spacecraft to the desired location at the entry interface altitude with a mean error of 12.1 km and 99.7% of cases below 100 km.

Nonconvex trajectory optimization is at the core of designing trajectories for complex autonomous systems. A challenge for nonconvex trajectory optimization methods, such as sequential convex programming, is to find an effective warm-starting point to approximate the nonconvex optimization with a sequence of convex ones. We introduce a first-order method with filter-based warm-starting for nonconvex trajectory optimization. The idea is to first generate sampled trajectories using constraint-aware particle filtering, which solves the problem as an estimation problem. We then identify different locally optimal trajectories through agglomerative hierarchical clustering. Finally, we choose the best locally optimal trajectory to warm-start the prox-linear method, a first-order method with guaranteed convergence. We demonstrate the proposed method on a multi-agent trajectory optimization problem with linear dynamics and nonconvex collision avoidance. Compared with sequential quadratic programming and interior-point method, the proposed method reduces the objective function value by up to approximately 96% within the same amount of time for a two-agent problem, and by 98% for a six-agent problem.

This article presents an algorithm to perform self-calibration of cable-driven parallel robots (CDPRs), where the CDPR’s end-effector pose is estimated in conjunction with the calibration of biases in CDPR’s measurements. Two new metrics, known as the position dilution of precision (PDOP) and orientation dilution of precision (ODOP), are introduced as a means to quantify the quality of data collected with regards to self-calibration. These metrics are based on a covariance matrix that is computed online as part of the proposed self-calibration algorithm, which results in the PDOP and ODOP directly corresponding to the standard deviation of the position and orientation errors, respectively. These metrics are used to intuitively select which data points contribute to improved calibration, resulting in a computationally efficient algorithm requiring few data points to maintain accurate calibration. In addition, the PDOP and ODOP provide a means to assess when sufficient calibration data have been collected. Numerical results involving an inverse kinematic simulation with rigid cables and a dynamic simulation with flexible cables indicate that the proposed algorithm is capable of performing self-calibration in a computationally efficient manner. Moreover, the simulation results indicate that the proposed PDOP and ODOP metrics result in smaller position and orientation errors when used to prune the dataset compared to the observability indices found in the literature. Accuracy of the proposed algorithm is also confirmed through experiments when compared to ground-truth pose data.

The flight testing of hypersonic vehicles is challenging due to the nonlinear, uncertain, and possibly unstable dynamics of these vehicles. This paper presents a control synthesis method for a hypersonic vehicle with the purpose of guaranteeing robust stability during flight testing when accurate analytic vehicle models are unavailable. Conventional model-based approaches typically rely on curve fitting of numerical simulation and test data, which can introduce inaccuracies. Our proposed approach assumes knowledge of the linear form of the ordinary differential equation and uses quadratic constraints to bound sampled data that accounts for the nonlinear and uncertain portion of the model for controller synthesis by iteratively solving convex semidefinite programs. A numerical example demonstrating the effectiveness of the proposed method is performed before applying the technique to a nonlinear hypersonic vehicle found in the literature. Using the synthesized stabilizing controller, we demonstrate that the vehicle states remain within a certified bound given a known harmonic excitation when initiated from a quantified set of allowable initial conditions. Based on these simulation results, our proposed control synthesis method shows promise in ensuring robustness when performing hypersonic vehicle flight testing.

The continued exploration of Mars will require a greater number of in-space assets to aid interplanetary communications. Future missions to the surface of Mars maybe augmented with stationary satellites that remain overhead at all times as a means of sending data back to Earth from fixed antennae on the surface. These areostationary satellites will experience several important disturbances that push and pull the spacecraft off of its desired orbit. Thus, a station-keeping control strategy must be put into place to ensure the satellite remains overhead while minimizing the fuel required to elongate mission lifetime. This paper develops a model predictive control policy for areostationary station keeping that exploits knowledge of non-Keplerian perturbations in order to minimize the required annual station-keeping 4v. The station-keeping policy is applied to a satellite placed at various longitudes, and simulations are performed for an example mission at a longitude of a potential future crewed landing site. Through careful tuning of the controller constraints, and proper placement of the satellite at stable longitudes, the annual station-keeping 4v can be reduced relative to a na & iuml;ve mission design.

Drag-modulation has been proposed for trajectory control of spacecraft in low-Earth orbit for uses such as formation keeping, targeted reentry and constellation phasing. However, using changes in aerodynamic drag to control a spacecraft requires knowledge of the atmospheric density in order to predict the drag force being applied. Due to modeling errors and inaccuracies in space weather forecasting, there will be a difference between the predicted density used to plan the trajectory and the true density encountered in-flight. This density prediction error causes the spacecraft to depart from the intended trajectory. This paper proposes the use of an extended Kalman filter along with a linear model of a spacecraft's motion relative to a planned trajectory to estimate the density prediction error. The estimated density can then be used to improve the performance of a drag-modulated control strategy or as measurements to improve atmosphere models. The proposed method is tested in simulation and found to be capable of estimating the time-varying density error caused by a space weather forecasting error. Estimated values of the density error are then shown to significantly improve the accuracy of state predictions made by the linear model.

Modeling the response of nonlinear structures due to random excitation is crucial for the design of mechanical systems, including the estimation of loading on mechanical joints and the fatigue life of nonlinear components. This chapter presents a method for bounding the maximum variance of the output response of a nonlinear system under random excitation of known power spectral density. The proposed approach leverages integral quadratic constraints (IQCs) that enclose the relationship between inputs and outputs of the nonlinearity sufficiently for analysis. While IQCs have traditionally been employed in robust control to analyze stability and performance, recent advancements have extended its applications to analyzing optimization algorithm rate of convergence and stability of transitional flows. In this chapter, we explore an optimization-based algorithm that harnesses different IQCs to bound the nonlinearities in the system. To validate the efficacy of the proposed algorithm, we apply it to the analysis of the Duffing equation, a well-known nonlinear oscillator. Results demonstrate the effectiveness of the algorithm in bounding the maximum variance of the system's response and its potential for application in the design and analysis of nonlinear structures subject to random vibration.

The paper presents a convex-optimization-based approach to synthesize robust full-state feedback controllers in the presence of probabilistic parametric uncertainty. The known probability distribution of the uncertain parameters is used to determine probabilistic sector bounds on the uncertainty. The proposed synthesis method results in a controller that ensures robust stability with high probability, while maximizing closed-loop performance for the most likely values of uncertainty. The method involves iteratively solving semidefinite programs within a bisection or coordinate descent scheme. A numerical example demonstrates the performance improvement achieved by the proposed method in the presence of probabilisitic parametric uncertainty compared to a controller designed with the typical assumption of uniform uncertainty distributions.

This paper presents the dynamic modeling, trajectory optimization, and control of the Cost- and Risk-Reducing Quadcopter System (CRQS, pronounced ``circus''). The CRQS is designed to mature novel guidance and control algorithms for launch vehicle and planetary landing systems. The components of the testbed---a quadcopter, a flexible inverted pendulum with an end mass, and a hanging pendulum---are modeled as separate bodies, then constrained together in the same manner as the physical prototype. An optimal trajectory is generated to softly land the CRQS at a desired location based on the booster soft-landing algorithm presented in existing literature. An inner-loop linear quadratic regulator with tracking is synthesized to stabilize the CRQS and have it track the trajectory. Four different configurations of the CRQS with progressively added features are numerically simulated. The results demonstrate the CRQS's ability to capture the dynamic features of launch vehicles and landing systems that other platforms do not, which often need to be considered when synthesizing guidance and control strategies.

Science instruments often take up a great amount of power and space within small satellites, which is drawn away from other components including attitude control hardware. This paper explores attitude control of a CubeSat in a dual-spin-stabilized configuration using magnetic actuation, which requires only one reaction wheel and three magnetic torque rods as actuators. The attitude dynamics are described, including important environmental perturbations in low-Earth orbit. This complete configuration is tested in an example inertial pointing mission similar to two university small-satellite projects, where it is assumed that the satellite is able to deviate from its nominal pointing attitude within some allowable pointing cone. Results from a carefully-tuned LQR control law and two different model predictive control (MPC) policies are compared, including linear-quadratic MPC and quadratically-constrained MPC. The MPC policies are equivalent except for the constraint on allowable pointing drift. It was found that MPC can explicitly account for the state and control constraints while utilizing drift within the allowable pointing cone to minimize control effort. The torque rod control input using an MPC policy was reduced by about 5-10x compared to the LQR control law.

This article presents a pose tracking controller for a six degree-of-freedom (DOF) overconstrained cable-driven parallel robot (CDPR). The proposed control method uses an adaptive feedforward-based controller to establish a passive input–output mapping for the CDPR. This is used alongside a linear time-invariant (LTI) strictly positive real (SPR) feedback controller to guarantee robust closed-loop input–output stability and asymptotic pose trajectory tracking via the passivity theorem. A novelty of the proposed controller is its formulation for use with a range of payload attitude parameterizations, including any unconstrained attitude parameterization, the quaternion, or the direction cosine matrix (DCM). The performance and robustness of the proposed controller is demonstrated through numerical simulations of a CDPR with rigid and flexible cables models. The results show that making use of a multiplicative computation of the pose error, such as when the quaternion or DCM is used within the control law, results in better performance compared to the use of linearized Euler-angle parameterization often used for control of CDPR.

This work provides a comprehensive comparison of four mixed H-2-H-infinity-optimal control synthesis methodologies for dual-stage hard disk drives (HDD). Combinations of the commonly-used H-2 and H-infinity objective functions and constraining metrics on the voice-coil motor (VCM), piezoelectric (PZT) actuator, and the position error signal (PES) drive the comparative analysis to better understand the control tradeoffs involved in their choice. The controllers are given identical design inputs and are synthesized using linear-matrix-inequality-based optimization. A simulated disturbance environment is used to analyze the closed-loop frequency response, and demonstrate the performance and benefits of each control method. This work demonstrates where each of the constraint metrics excel, which serves as a basis for tailored design based on the need of the HDD control engineer. Copyright (c) 2024 The Authors.

Dissipativity is a powerful tool in control design as it can be used to ensure closed-loop stability using open-loop input-output properties. This paper presents a framework to estimate the QSR-dissipative parameters of a discrete-time system from estimates of either the power spectral response or transfer function of the system. Specific methods are presented for estimating the input feedforward passivity index, conic sector bounds and L2-gain of the system. Methods are also presented to propagate the bound on the worst-case error from the power spectral response to these parameters with high probability. Numerical simulations are performed using the proposed methods on a randomly generated system. The estimators for the QSR-dissipative parameters closely match the true values even when the signal-to-noise ratio is small, while the computed worst-case error bound is not violated in any simulation.

This paper presents a modular dynamic modeling approach to simulate a solar sail embedded with actuated cables within its flexible structure. The cables are routed along the length of the flexible booms that hold the solar sail membrane in such a manner that tensioning the cables results in a bending deformation of the booms. This provides a mechanism where actuation of the cables can be used to create an imbalance in solar radiation pressure (SRP) on the sail and thus, impart SRP torques that can be used for momentum management of the solar sail. The modular aspect of the modeling and simulation approach presented in this paper allows for various designs of this cable-actuated solar sail concept to be assessed without having to re-derive the system dynamics. The dynamic model is developed by first deriving equations of motion of the various components of the solar sail, including a rigid hub, four flexible booms (modeled as Euler-Bernoulli beams), and a flat sail membrane, then modularly constraining the components together without the need for Lagrange multipliers. Simulation results are included that demonstrate how SRP torques can be induced by tensioning the solar sail's cables.

We propose a digitally assisted analog computing circuit for real-time model predictive control (MPC) of a DCDC buck converter. The computing circuit comprises analog elements for speed and digital components for programmability. It implements gradient-flow dynamics for a penalty-based reformulation of the quadratic optimization problem corresponding to the original MPC formulation. The MPC problem is set up to regulate output voltage while explicitly enforcing constraints on the buck converter’s inductor current and duty cycle. Simulation results in a closed-loop configuration demonstrate superior dynamic response with lower settling time and overshoot compared to the Type-III controller and linear quadratic regulator (LQR). The proposed approach achieves accuracy similar to the numerically computed optimal solution from the interior-point-convex algorithm of MATLAB’s quadprog solver while offering real-time implementation capability.

This paper presents a passivity-based adaptive control method for a 5 degree-of-freedom (DOF) tower crane that guarantees robust payload trajectory tracking. The 5-DOF tower crane system considered in this work features three actuated degrees of freedom (including a varying-length hoist cable) and two unactuated degrees of freedom in the hoist cable sway. The proposed controller includes an adaptive feedforward-like control input that is used to ensure that the tower crane features an output strictly passive input–output mapping. The Passivity Theorem is invoked to guarantee closed-loop input–output stability for any output strictly passive negative feedback controller. A novel approach is developed to bound the time derivative of the system’s mass matrix, which is a critical aspect of the proof of passivity. Experimental tests are performed, which demonstrate the effectiveness of the control law on a small-scale three-dimensional tower crane.

This paper presents a robust passivity-based payload trajectory tracking control method for redundantly-actuated flexible robotic manipulators. The proposed approach is based on µ-tip control, which involves the use of a modified system output to ensure a passive input-output mapping. This work distinguishes itself from prior implementations of µ-tip control with flexible manipulators by demonstrating the generality with which redundant actuation can be accounted for. In particular, it is shown that prior load-sharing-parameter-based approaches are a special case of a more general kinematic constraint that is to be enforced to ensure passivity. Numerical results with an overactuated cable-driven parallel robot demonstrate the performance of the proposed µ-tip control method.

There is an ever-growing need for sustainable and reliable telecommunications between Earth and Mars, especially as future crewed missions come into view. Areostationary Mars Orbits (AMOs) are geostationary-equivalent orbits that would allow for reliable communication back to Earth from the surface of the red planet via satellites consistently overhead. Due to the significant gravitational perturbations around Mars, an efficient station keeping policy is needed to minimize fuel consumption, lengthen mission time, and ensure that the satellite remains in its desired position overhead. A high-fidelity orbital model is developed that includes disturbances from high-order spherical harmonic gravitational terms and the gravitational perturbations due to celestial bodies such as the Sun and the Martian moons Phobos and Deimos. This paper formulates two model predictive control (MPC) station keeping policies—linear-quadratic MPC and nonlinear MPC—and discusses the benefits and limitations of each. These proposed methods of MPC satisfy the station keeping requirements while setting new benchmarks for annual Δv required to maintain the satellite within a prescribed station keeping window. Numerical simulations demonstrate that the nonlinear MPC policy provides a significant reduction in the fuel required for AMO station keeping at specific longitudes compared to a linear-quadratic MPC implementation.