Index — Controls

Auto-extracted reference table: authors · year · title · DOI/locator, taken verbatim from the notes below. Nothing invented; — = field not given in the source. Where an entry is filed under a year header that differs from its citation, the Year column follows the citation text. Sorted in your four batches, by year.

Very Early works: year ≤ 2000

Early works: 2000 < year ≤ 2010

Semi-Early works: 2010 < year ≤ 2020

Recent works: year > 2020

Original notes

Very Early works: year <= 2000 1986

• Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mishchenko E.F. The mathematical theory of optimal processes. Gordon and Breach Science Publishers, Montreux (1986)

1989 • Ortega R, Spong MW. 1989. Adaptive motion control of rigid robots: a tutorial. Automatica 25:877–88 1991 • Walker M, Wee LB. 1991. Adaptive control of space-based robot manipulators. IEEE Trans. Robot. Autom. 7:828–35 ○ presented a passivity-based adaptive tracking controller that meets the global asymptotic convergence condition presented by Ortega & Spong 1993 • Egeland, O., & Sagli, J. R. (1993). Coordination of Motion in a Spacecraft/ Manipulator System. The International Journal of Robotics Research, 12(4), 366–379. https://doi.org/10.1177/027836499301200404 ○ A control scheme for the coordination of motion in a spacecraft/manipulator system is presented. It is shown how end-effector motion can be decoupled from satellite motion, satellite rotation, or total system momentum by selecting suitable generalized speeds for the satellite. The schemes are based on recursive calculation of kinematics and dynamics, and 12 degrees of freedom can be controlled without excessive computational effort. Feedback linearization and decoupling of end-effector motion and total system momentum are discussed in detail. The satellite controller can then be developed in dependently of the manipulator controller, and reaction jets and momentum wheels are used only to reposition the satellite. The end effector can be controlled accurately with a high bandwidth, while a slow, gross positioning can be used for the satellite. The resulting controller is very efficient in terms of fuel. The spacecraft/manipulator system is regarded as a redundant manipulator of the macro-micro type with 12 degrees of freedom, and a redundancy resolution scheme based on the augmented task space approach is used to generate the position and orientation reference for the spacecraft. The proposed controller was simulated with a 12-degrees-of-freedom model that was generated with a recursive formulation of the Jacobians. • Carignan, C. R., & Akin, D. L. (2000). The reaction stabilization of on-orbit robots. IEEE Control Systems, 20(6), 19–33. https://doi.org/10.1109/37.887446 ○ The focus of this article is to examine the reaction moment effect of satellite-based manipulators and to investigate the feasibility of stabilizing the base platform during arm operations. The goal is not to advance the state of the art in adaptive control, but rather to illustrate the benefits of autonomous attitude stabilization through reaction moment compensation. A derivation of vehicle body dynamics using reaction wheels and thrusters as the primary input sources is given. The modifications to the Newton-Euler method necessary to accommodate a manipulator arm with a free-flying base are then outlined. Next, a quaternion-based feedback regulator design is adopted. 1994

• Boyd S., Ghaoui L.E., Feron E., Balakrishnan V. Linear matrix inequalities in system and control theory Society for Industrial and Applied Mathematics 
    ○ semidefinite program (SDP) class enables optimization over the space of positive semidefinite matrices, which leads to many important robust control design algorithms

1995 • Senda K, Murotsu Y, Nagaoka H, Mitsuya A. 1995. Attitude control for free-flying space robot with CMG (Control Moment Gyroscopes). In Guidance, Navigation, and Control Conference, pp. 1494–502. Reston, VA: Am. Inst. Aeronaut. Astronaut. ○ The nonlinear nature of the free-flying SMRS dynamics is particularly evident when the spacecraft-mounted robot executes fast maneuvers, which, for instance, may bring about flexibility effects or induce fuel sloshing. As a consequence, numerous nonlinear control approaches have been investigated by the community to remedy these effects. Senda et al. (67) derived and tested two nonlinear controllers, using control moment gyros to regulate the attitude of the base: a Lyapunov-type controller that included an integral term for disturbance rejection and an exact input–output feedback linearization. When comparing the two approaches, the authors highlighted that the latter leads to an easier design procedure. ○ A common limitation of the aforementioned studies is that they implicitly assume exact knowledge of the system. Adaptive and robust methods remove such underlying assumptions and tackle uncertainties within the same control framework. 1998

• Betts J.T. Survey of numerical methods for trajectory optimization. Journal of Guidance, Control, and Dynamics, 21 (2) (1998),
    ○ eloquent, albeit somewhat dated, treatise on trajectory optimization methods.

1999 • Senda K, Nagoaka H, Murotsu Y. 1999. Adaptive control of free-flying space robot with position/attitude control system. J. Guid. Control Dyn. 22:488–90 ○ The well-known Slotine–Li regressor matrix (77), originally developed in the context of ground-fixed payload manipulation, was revisited by Senda et al. (78) and adapted to the case of a stabilized spacecraft grasping an unknown payload with a robotic arm. The stability of the closed-loop system, including both satellite and manipulator variables, was proved through Lyapunov’s second method. 2000 • Mayne D., Rawlings J., Rao C., Scokaert P. Constrained model predictive control: Stability and optimality. Automatica, 36 (6) (2000), pp. 789-814, 10.1016/s0005-1098(99)00214-9 ○ optimization is one of the few suitable methods (and is perhaps the most natural one) to directly impose system constraints Early works: 2000 < year <= 2010 2005 • Skogestad S., Postlethwaite I. Multivariable feedback control: Analysis and design. Wiley ○ the semidefinite program (SDP) class enables optimization over the space of positive semidefinite matrices, which leads to many important robust control design algorithms

2006 • D’Amico, S., and Montenbruck, O., “Proximity Operations of Formation Flying Spacecraft Using an Eccentricity/Inclination Vector Separation,” Journal of Guidance, Control and Dynamics, Vol. 29, No. 3, 2006, pp. 554–563. ○ one-orbit minimum distance plays a crucial role to assess the safety of a formation in the presence of navigation uncertainties in the along-track direction

• Carson III J., Açıkmeşe B. A model-predictive control technique with guaranteed resolvability and required thruster silent times for small-body proximity operations. AIAA guidance, navigation, and control conference
    ○ Solving nonconvex optimization problems will be required for many foreseeable space vehicles 

• Antsaklis P.J., Michel A.N. Linear systems

Semi-Early works: 2010 < year <= 2020 2012

• Trélat E. Optimal control and applications to aerospace: Some results and challenges Journal of Optimization Theory and Applications
    ○ a comprehensive survey of modern optimal control theory and indirect methods for aerospace problems, covering geometric optimal control, homotopy methods, and favorable properties of orbital mechanics that can be leveraged for trajectory optimization

2013

• Domahidi A., Chu E., Boyd S. ECOS: An SOCP solver for embedded systems 2013 European control conference (ECC), IEEE (2013), pp. 3071-3076,
    ○ SOCP is the most general class of problems that state-of-the-art algorithms can solve with high reliability and rigorous performance guarantees 

• Achterberg T., Wunderling R. Mixed integer programming: Analyzing 12 years of progress Facets of combinatorial optimization, Springer Berlin Heidelberg (2013)
    ○ This leads to the mixed-integer convex program (MICP) class, where binary variables are introduced to emulate discrete switches, such as those of valves, relays, or pulsing space thrusters
    ○ the optimization community has had many successes in finding practical solution methods even for these most challenging problems

2014 • Morgan D., Chung S.-J., Hadaegh F.Y. Model predictive control of swarms of spacecraft using sequential convex programming. J. Guid. Control Dyn., 37 (6) (2014) ○ Of great interest in the trajectory optimisation methods applied to the proximity scenarios are the convex formulations of the guidance problem. These approaches provide a computationally efficient and robust strategy, which are extremely suitable for the high autonomy requirements involved in proximity operations • Liu X. and Lu P., “Solving Nonconvex Optimal Control Problems by Convex Optimization,” Journal of Guidance, Control, and Dynamics, Vol. 37, No. 3, 2014,

• Dueri D., Zhang J., Açıkmeşe B. Automated custom code generation for embedded, real-time second order cone programming IFAC Proceedings Volumes, 47 (3) (2014)
    ○ SOCP is the most general class of problems that state-of-the-art algorithms can solve with high reliability and rigorous performance guarantees 

2015 • Palacios L., Ceriotti M., Radice G. Close proximity formation flying via linear quadratic tracking controller and artificial potential function. Adv. Space Res., 56 (10) (2015) ○ APF approach to optimal design • Gaias G., D’Amico S. Impulsive maneuvers for formation reconfiguration using relative orbital elements J. Guid. Control Dyn., 38 (6) (2015) 2016 • P. Huang et al., “Attitude takeover control for post-capture of target spacecraft using space robot”, Aerosp. Sci. Technol., vol. 51, pp. 171-180, 2016. ○ designed a reconfigurable control system based on optimization method, which can quickly redistribute the inertial distribution to achieve attitude takeover control after the dual-arm space robot captures an external objective. ○ micronano space robot can be regarded as a suspended multirigid body problem that is hinged to each other, including a satellite base and a number of chained robotic arms connected to it 2017

• Tsiotras P., Mesbahi M. Toward an algorithmic control theory. Journal of Guidance, Control, and Dynamics, 40 (2) (2017), pp. 194-196, 
    ○ optimization is indeed one of the most compelling frameworks for finding feasible solutions in the presence of challenging constraints
• Dueri D., Açıkmeşe B., Scharf D.P., Harris M.W. Customized real-time interior-point methods for onboard powered-descent guidance. Journal of Guidance, Control, and Dynamics,
    ○ SOCP is the most general class of problems that state-of-the-art algorithms can solve with high reliability and rigorous performance guarantees  
• Liu X., Lu P., Pan B. Survey of convex optimization for aerospace applications Astrodynamics, 1 (1) (2017)
    ○ survey the various appearances of lossless convexification and sequential convex programming in aerospace guidance methods
• Eren U., Prach A., Koçer B.B., Raković S.V., Kayacan E., Açıkmeşe B. Model predictive control in aerospace systems: Current state and opportunities. Journal of Guidance, Control, and Dynamics, 40 (7) (2017)
    ○  cover extensively the topic of model predictive control for aerospace applications, where optimization is solved recursively to compute control actions

2018 • R. Lampariello et al., “Tracking control for the grasping of a tumbling satellite with a free-floating robot”, IEEE Robot. Automat. Lett., vol. 3, no. 4, pp. 3638-3645, Oct. 2018. ○ used optimal control to provide an offline motion planner for the space robot and adjust the reference trajectory online • S. Jia et al., “Maneuver and active vibration suppression of free-flying space robot”, IEEE Trans. Aerosp. Electron. Syst., vol. 54, no. 3, pp. 1115-1134, Jun. 2018. • space orientation tasks of microsatellites can be divided into two parts: • 1) orientation of the satellite base; • 2) orientation of the end effectors (such as rotating solar sails, antennas, or cameras) • This work studies the maneuver control and vibration suppression of a flexible free-flying space robot using variable-speed control moment gyros as actuators. A novel flexible space manipulator is designed. The dynamics of the flexible multibody system is derived by using Kane method. Based on the singular perturbation approach, the dynamics of the flexible manipulator is decoupled into a slow subsystem and a fast subsystem. The slow subsystem is associated with the rigid motion dynamics, and the fast subsystem is related to the link flexible dynamics. A composite control strategy is proposed as a combination of two controllers for these subsystems. An adaptive sliding mode controller is designed for the slow subsystem, and an adaptive controller is designed for the fast subsystem. Uncertainty estimation can be achieved by the adaptive terms of the composite controller. A weighted robust pseudo-inverse steering law is proposed for the variable-speed control moment gyros. Numerical results demonstrate that the proposed composite controller is robust to parameter uncertainties and external disturbances. • proposed composite controller can guarantee not only the maneuver control of the rigid motion but also the vibration suppression of the flexible links even in the presence of parameter uncertainties and external disturbances. • Mao Y., Dueri D., Szmuk M., Açıkmeşe B. Convexification and real-time optimization for MPC with aerospace applications. Handbook of model predictive control, • lossless convexification, sequential convex programming, and solver customization for real-time computation.
• Tutorial on SCvx • Shirazi A., Ceberio J., Lozano J.A. Spacecraft trajectory optimization: A review of models, objectives, approaches and solutions • thorough discussion on the general philosophy and specific methods and solutions for in-space trajectory optimization. • 2019 • V. Muralidharan, M.R. Emami Rendezvous and attitude synchronization of a space manipulator J. Astronaut. Sci., 66 (2019), ○ The control of a spacecraft equipped with a six-degree-of-freedom robot manipulator is studied in this paper. The objective is to rendezvous and synchronize with a satellite to facilitate inspection, servicing or de-orbiting. The space manipulator dynamics model with global parameterization on the configuration manifold is derived and used for designing asymptotically-stable control laws, so that they are valid globally in the configuration manifold. The control system consists of a sliding-mode rendezvous controller as well as a geometric attitude synchronization and a model-based servo control for the robot manipulator. The gains of the sliding-mode controller dictate a user-defined upper-bound on the thrust force. The attitude synchronization controller, concurrently with the rendezvous controller, is capable of micro-orbiting the space manipulator around spinning or tumbling satellites. It is observed through the simulations that the controller consumes limited amount of propellant, and it is feasible to use it for either a re-fueling (larger mass) or a de-orbiting (smaller mass) space manipulator. ○

• Szmuk M., Malyuta D., Reynolds T.P., Mceowen M.S., Acikmese B. Real-time quad-rotor path planning using convex optimization and compound state-triggered constraints. 2019 IEEE/RSJ international conference on intelligent robots and systems (IROS), IEEE (2019), 10.1109/iros40897.2019.8967706

• Zhou D., Zhang Y., Li S. Receding horizon guidance and control using sequential convex programming for spacecraft 6-DOF close proximity. Aerospace Science and Technology, 87 (2019), pp. 459-477

2020 • S. Jia and J. Shan, “Continuous integral sliding mode control for space manipulator with actuator uncertainties”, Aerosp. Sci. Technol., vol. 106, pp. 106192, 2020. ○ Spacecraft braking is another important application scenario of micronano space robots and it is often difficult to guarantee an absolute zero initial angular momentum after the spacecraft is separated from the delivery vehicle into space. Many spacecrafts lose ground telemetry connections or cause control system divergence due to the high-speed spin caused by this large initial angular momentum • Mohamed, A., Saaj, C., & Seddaoui, A. (2020). Linear controllers for free-flying and controlled-floating space robots: a new perspective. Aeronautics and Aerospace Open Access Journal, 4(3), 97–114. https://doi.org/10.15406/aaoaj.2020.04.00112 ○ https://medcraveonline.com/AAOAJ/AAOAJ-04-00112.pdf ○ presents the dynamic model of the space robot and a three-stage control algorithm for this highly dynamic non-linear system. In this approach, feed-forward compensation and feed-forward linearization techniques are used to decouple and linearize the highly non-linear system respectively. This approach allows the use of the linear Proportional-Integral-Derivative (PID) controller and Linear Quadratic Regulator (LQR) in the final stages. Moreover, this paper covers a simulation-based trade-off analysis to determine both proposed linear controllers’ efficacy. This assessment considers precise trajectory tracking requirements whilst minimizing power consumption and improving robustness during the close-range operation with the target spacecraft. • Foust R., Chung S.-J. and Hadaegh F. Y., “Optimal Guidance and Control with Nonlinear Dynamics Using Sequential Convex Programming,” Journal of Guidance, Control, and Dynamics, Vol. 43, No. 4, 2020 ○ The optimal control problem is transformed to a convex optimization problem by using the discrete dynamics and convexifying the collision constraint about a nominal trajectory, given the full trajectory of the neighboring observer spacecraft 𝑗, (Nakka et al) • Giordano, A. M., Dietrich, A., Ott, C., & Albu-Schäffer, A. (2020). Coordination of thrusters, reaction wheels, and arm in orbital robots. Robotics and Autonomous Systems, 131, 103564-. https://doi.org/10.1016/j.robot.2020.103564 ○ A fuel-efficient control strategy for a manipulator-equipped spacecraft is presented. The strategy uses the thrusters, the reaction wheels, and the arm drives in a coordinated way to limit the use of the thrusters and achieve ideally zero fuel consumption in contact-free maneuvering. The thrusters are activated automatically only after contact, to stabilize the inertial motion of the system. The controller regulates the translation of the center-of-mass (CoM) of the whole space robot, the rotation of the spacecraft, and the pose of the end-effector (EE) in a decoupled way, utilizing the thrusters to control the CoM translation only and the remaining actuators to control the rotation and end-effector coordinately. The method is validated experimentally using a hardware-in-the-loop simulator composed of a seven degrees-of-freedom (DOF) arm mounted on a 6DOF simulated spacecraft. Numerical simulations with discrete thrusters assess the fuel efficiency of the proposed strategy. •Coordinated control of the attitude of the spacecraft, the position of the global CoM, and the end-effector.•Dynamics transformation with total decoupling of external and internal motion.•Fuel-efficient thrusters activation via decoupled actuation of thrusters, reaction wheels, and arm.•3D Hardware-in-the-loop robotic simulation.

Recent works: year > 2020 2021 • R. Jin et al., “LPV-Based offline model predictive control for free-floating space robots”, IEEE Trans. Aerosp. Electron. Syst., vol. 57, no. 6, pp. 3896-3904, Dec. 2021. • B. Moghaddam Monazzah and R. Chhabra, “On the guidance navigation and control of in-orbit space robotic missions: A survey and prospective vision”, Acta Astronautica, vol. 184, pp. 70-100, 2021. • Malyuta, D., Yu, Y., Elango, P., & Açıkmeşe, B. (2021). Advances in trajectory optimization for space vehicle control. Annual Reviews in Control, 52, 282–315. https://doi.org/10.1016/j.arcontrol.2021.04.013 ○ Space mission design places a premium on cost and operational efficiency. The search for new science and life beyond Earth calls for spacecraft that can deliver scientific payloads to geologically rich yet hazardous landing sites. At the same time, the last four decades of optimization research have put a suite of powerful optimization tools at the fingertips of the controls engineer. As we enter the new decade, optimization theory, algorithms, and software tooling have reached a critical mass to start seeing serious application in space vehicle guidance and control systems. This survey paper provides a detailed overview of recent advances, successes, and promising directions for optimization-based space vehicle control. The considered applications include planetary landing, rendezvous and proximity operations, small body landing, constrained attitude reorientation, endo-atmospheric flight including ascent and reentry, and orbit transfer and injection. The primary focus is on the last ten years of progress, which have seen a veritable rise in the number of applications using three core technologies: lossless convexification, sequential convex programming, and model predictive control. The reader will come away with a well-rounded understanding of the state-of-the-art in each space vehicle control application, and will be well positioned to tackle important current open problems using convex optimization as a core technology. • Foust, Rebecca, et al. “Optimal Guidance and Control with Nonlinear Dynamics Using Sequential Convex Programming.” Journal of Guidance, Control, and Dynamics, vol. 43, no. 4, 2020, pp. 633–44, https://doi.org/10.2514/1.G004590. • This paper presents a novel method for expanding the use of sequential convex programming (SCP) to the domain of optimal guidance and control problems with nonlinear dynamics constraints. SCP is a useful tool in obtaining real-time solutions to direct optimal control, but it is unable to adequately model nonlinear dynamics due to the linearization and discretization required. As nonlinear program solvers are not yet functioning in real-time, a tool is needed to bridge the gap between satisfying the nonlinear dynamics and completing execution fast enough to be useful. Two methods are proposed, SCP with nonlinear dynamics correction (SCPn) and modified SCPn (M-SCPn), which mixes SCP and SCPn to reduce runtime and improve algorithmic robustness. Both methods are proven to generate optimal state and control trajectories that satisfy the nonlinear dynamics. Simulations are presented to validate the efficacy of the methods as compared with SCP.

2022 • Fu, J., Chen, L., Zhang, D., Zhang, J., & Shao, X. (2022). Disturbance Observer-Based Prescribed Performance Predictive Control for Spacecraft On-Orbit Inspection. Journal of Guidance, Control, and Dynamics, 45(10), 1873–1889. https://doi.org/10.2514/1.G006406 ○ Spacecraft on-orbit inspection provides a prerequisite for the subsequent autonomous proximity operations. To fulfill the mission, robust constrained control algorithms for relative position tracking and attitude adjustment should be employed to handle the nonlinear coupled dynamics, system constraints, and external disturbances. In this paper, a robust nonlinear model predictive control (NMPC) scheme with prescribed performance based on a fixed-time neural network disturbance observer is proposed. Predefined tracking performance requirements are achieved, and, meanwhile, safety and stability are guaranteed. By exploiting the prescribed performance control technique, the proposed NMPC structure is capable of establishing a quantitative relationship between design parameters and certain prespecified performance values. Moreover, the proposed fixed-time neural network disturbance observer shows superiority in the disturbance estimations due to the property of universal approximation and fixed-time convergence. To illustrate the capabilities of our algorithm, comparison simulation tests concerning with prescribed performance and disturbance estimating are presented. Selection of tuning parameters is discussed, and computational load of the proposed algorithm is profiled. • Tsiotras et al. Spacecraft-Mounted Robotics. (2022) ○ https://www.annualreviews.org/docserver/fulltext/control/6/1/annurev-control-062122-082114.pdf?expires=1727999925&id=id&accname=guest&checksum=CE1CEF69865333B2023EAB425A146FDF ○ review the basic current approaches for modeling and control of spacecraft-mounted robotic systems to introduce some new developments in terms of modeling and control of spacecraft-mounted robotic manipulators using the language of hypercomplex numbers (dual quaternions). ○ • Sai, H., Xia, C., Li, H., & Xu, Z. (2022). Predefined-time Sliding Mode Control for Attitude Tracking Control of Space Free-flying Robots. 2022 IEEE International Conference on Mechatronics and Automation (ICMA), 292–297. https://doi.org/10.1109/ICMA54519.2022.9856061 ○ Aiming at the attitude tracking control of space free-flying robots, a predefined-time sliding mode control (PTSMC) scheme is proposed. First, the kinematic and dynamical models of the space free-flying robot are constructed, and the uncertainties and external perturbations of the system are considered. Then, a predefined-time sliding surface is constructed. A nonconservative PTSMC scheme is designed based on this surface, and the discontinuous chattering is alleviated by the boundary layer technique. With the Lyapunov theory, the predefined-time stability of the proposed controller is demonstrated. Finally, the numerical simulation shows that compared with the existing predefined-time controllers, the upper bound on the settling time of the proposed controller is more nonconservative and has higher tracking accuracy than the traditional PD control and the nonsingular terminal sliding mode control. Meanwhile, the effectiveness of the controller is illustrated by the attitude tracking experiment of a 3-DOF air-floating robot. • Benedikter et al. Convex Approach to Covariance Control with Application to Stochastic Low-Thrust Trajectory Optimization ○ This paper outlines a novel approach to the design of optimal space trajectories under significant uncertainty. Finite-horizon covariance control, i.e., the steering of a system from an initial probability distribution to a desired one at a prescribed time, is employed to plan an optimal nominal path along with a robust feedback controller that compensates for exogenous in-flight disturbances. A mindful convexification strategy is devised to recast the nonlinear covariance control problem as a deterministic convex optimization problem. The convexification is based on a convenient change of variables that allows for relaxing the covariance matrix discrete-time propagation into a set of semidefinite cone constraints. While featuring a larger feasible space, the relaxed problem shares the same optimal solution as the original one. The lossless property of the relaxation is analytically proven by leveraging optimal control theory and discussed on the basis of numerical experiments. Monte Carlo campaigns are carried out to validate the in-flight performance of the attained control policies. 2023 • Dyba, F., Rybus, T., Wojtunik, M., & Basmadji, F. L. (2023). Active 6 DoF Force/Torque Control Based on Dynamic Jacobian for Free-Floating Space Manipulator. ○ In-orbit capture of a non-cooperative satellite will be a major challenge in the proposed servicing and active debris removal missions. The contact forces between the manipulator end-effector and the elements of the target object will occur in the grasping phase. ○ In this paper, an active 6 Degrees of Freedom (DoF) force/torque control method for manipulator mounted on a free-floating servicing satellite is proposed. The main aim of the presented method is to balance the relation between end-effector position and force along each direction in the Cartesian space. ○ The control law is based on the Dynamic Jacobian, which takes into account the influence of the manipulator motion on the state of the servicing satellite. The proposed approach is validated in numerical simulations with a simplified model of contact. Comparison with the classical Cartesian control shows that the active 6 DoF force/torque control method allows to obtain better positioning accuracy of the end-effector and lower control torques in manipulator joints in the presence of external forces. • Giordano et al. Quaternion-Based Non-Singular Terminal Sliding Mode Control for a Satellite-Mounted Space Manipulator (2023) https://ieeexplore-ieee-org.ezproxy.lib.torontomu.ca/stamp/stamp.jsp?tp=&arnumber=10159019 ○ This design is for the presence of large uncertainties and disturbances from eg. grasping an unknown target ○ It may be useful anyway ○ a robust control solution for a satellite equipped with a robotic manipulator is presented. ○ First, the dynamical model of the system is derived based on quaternions to describe the evolution of the attitude of the base satellite. ○ Then, a non-singular terminal sliding mode controller that employs quaternions for attitude control, is proposed for concurrently handling all the degrees of freedom of the system. ○ Moreover, an additional adaptive term is embedded in the controller to estimate the upper bounds of disturbances and uncertainties. ○ The result is a resilient solution able to withstand unmodelled dynamics and interactions. Lyapunov theory is used to prove the stability of the controller and numerical simulations allow assessing performance and fuel efficiency. ○ The system can be modeled as a chain of n + 1 rigid bodies, where n is the number of arm links. ○ In this letter a proximity operation scenario is evaluated. The target object, which is used as reference point, is supposed to be fixed in the inertial frame. This assumption is not too simplistic when considering close proximity operations that are much shorter than the orbital periods of the two bodies [1]. ○ In addition, no orbital or environmental disturbances are considered since they are deemed to be considerably smaller than those related to the dynamics of the actuators during such a time span.

• Wang et al. Model predictive control for close-proximity maneuvering of spacecraft with adaptive convexification of collision avoidance constraints. Advances in space research, 2023-01
    ○ This study investigated model predictive control (MPC) for close-proximity maneuvering of spacecraft. It is essential for a designed MPC to effectively handle collision avoidance between the servicer spacecraft and the client spacecraft, especially while the client is rotating. The rotating motion of the client leads to dynamic changes in the collision avoidance constraints, which increases the difficulty of optimizing the control input in the MPC framework. Therefore, this study presents a method to improve the performance and computational efficiency of MPC for rendezvous and docking with a nonrotating or rotating client. An ellipsoid is adopted to model the client’s keep-out zone (KOZ). Given the spherical KOZ of the servicer, an expanded ellipsoid is introduced to describe the KOZ for the center of mass of the servicer and modeled as a nonlinear constraint. The linearization method for reference points located at the expanded ellipsoid is adopted to convexify the nonlinear constraints. The reference points are adaptively determined according to the positions of the servicer, client, and expanded ellipsoidal KOZ. The resulting hyperplanes are then used to describe the collision avoidance constraints. By utilizing the aforementioned strategies, combined with the calculated reference points, an adaptive convex programming algorithm suitable for real-time implementation of MPC is derived. The performance of the proposed method is demonstrated through numerical simulations.
• Model predictive control for close-proximity maneuvering of spacecraft with adaptive convexification of collision avoidance constraints

2024 • Scalvini, A., Suarez, A., Nekoo, S. R., & Ollero, A. (2024). Finite-time state-dependent Riccati equation regulation of anthropomorphic dual-arm space manipulator system in free-flying conditions. Acta Astronautica, 216, 504–517. ○ regulating the pose of a free-flying dual-arm anthropomorphic space manipulator system (SMS) using a finite-time state-dependent Riccati equation (SDRE) controller. The proposed system finds applications in on-orbit satellite inspection, servicing, space structure assembly, and debris manipulation. ○ The dual-arm SMS presented in this work consists of two 7 degrees of freedom (DoF) robotic arms mounted on a free-flying spacecraft, resulting in a complex 20-DoF system. ○ Due to the high number of DoFs, advanced controller design and efficient computations are necessary. The finite-time SDRE controller relies on the state-dependent coefficient (SDC) parameterization matrices, which are nonlinear apparent linearizations of the dynamics. Conventionally, the computation of SDC matrices is offline and relies on the a priori derivation of the analytical equations governing the dynamics of the system. However, this strategy becomes computationally impractical for high DoF plants. ○ To overcome this issue and deliver a more viable solution, a numerical method to construct and update the SDC matrices at each time step is presented. This approach relies on a screw-theory-based recursive Newton–Euler algorithm designed to reconstruct the manipulator inertia and Coriolis matrices. These quantities are the building blocks of the SDC parameters used in the synthesis of the SDRE controller. • Wang, Z. (2024). A survey on convex optimization for guidance and control of vehicular systems. Annual Reviews in Control, 57(C), 100957-. https://doi.org/10.1016/j.arcontrol.2024.100957 ○ Guidance and control (G&C) technologies play a central role in the development and operation of vehicular systems. The emergence of computational guidance and control (CG&C) and highly efficient numerical algorithms has opened up the great potential for solving complex constrained G&C problems onboard, enabling higher level of autonomous vehicle operations. In particular, convex-optimization-based G&C has matured significantly over the years and many advances continue to be made, allowing the generation of optimal G&C solutions in real-time for many vehicular systems in aerospace, automotive, and other domains. In this paper, we review recent major advances in convex optimization and convexification techniques for G&C of vehicular systems, focusing primarily on three important application fields: (1) Space vehicles for powered descent guidance, small body landing, rendezvous and proximity operations, orbital transfer, spacecraft reorientation, space robotics and manipulation, spacecraft formation flying, and station keeping; (2) Air vehicles including hypersonic/entry vehicles, missiles and projectiles, launch/ascent vehicles, and low-speed air vehicles; and (3) Motion control and powertrain control of ground vehicles. Throughout the paper, we draw figures that illustrate the basic mission concepts and objectives, introduce key equations that characterize the feature of each class of problems and approaches, and present tables that summarize similarities and distinctions among the problems, ideas, and methods. Where available, we provide comparative analyses and reveal correlations between different applications and technical approaches. Finally, we identify open challenges and issues, discuss potential opportunities, and make suggestions for future research directions. • Tian et al. High-Precision Trajectory Tracking Control for Free-Flying Space Manipulators With Multiple Constraints and System Uncertainties (2024) ○ Precise motion control for free-flying space manipulators (FFSMs) plays an important role in space missions. However, system uncertainties and various physical constraints severely degrade the trajectory tracking performance. In order to tackle these difficulties, a fully actuated system approach (FASA)-based composite controller is developed, which consists of a nonlinear disturbance observer (NDO) in the inner loop and a high-precision trajectory controller in the outer loop. More specifically, the NDO is designed for tackling system uncertainties. Moreover, a gradient-based optimal parameter tuning method is developed for tuning the control gains of the composite controller. The satisfaction of physical constraints, which include angular constraints and actuator constraints can be guaranteed by the gradient-based optimal parameter tuning method. Therefore, the high-precision trajectory tracking performance, optimal control gains, angular constraints, and actuator constraints can be ensured simultaneously. Simulation results are presented to demonstrate the effectiveness of the proposed method. • Xie, Z., Chen, X., & Wu, X. (2024). Fixed time control of free-flying space robotic manipulator with full state constraints: a barrier-Lyapunov-function term free approach. Nonlinear Dynamics, 112(3), 1883–1915. https://doi.org/10.1007/s11071-023-09097-z a new sliding mode control scheme based on a fixed time disturbance observer is proposed to realize the fixed time coordinate motion control of SRM with full-state constraints. Firstly, the tracking error and error velocity at the novel sliding manifold can converge to the equilibrium within a fixed time without violating their state constraints. Then, the control law based on the fixed time disturbance observer is designed to achieve the sliding manifold within a fixed time, which simultaneously satisfies the state constraints during the approaching stage. Unlike the most existing state constraint control schemes, the proposed controller does not include any Barrier Lyapunov Function (BLF) terms of system states, and therefore the risk of controller outputting inappropriately high control commands is eliminated. Moreover, the proposed control scheme is compatible to the initial system states violating their constraints, which thereby removes the assumption of feasible initial states. Furthermore, the proposed sliding manifold solves the singularity issue by a continuously varying power of tracking error, which thereby does not need an additional switch mechanism of manifold compared to the conventional fixed time controllers. The stability of the proposed control scheme is proven by using the Lyapunov theory, and the effectiveness is verified by numerical simulations • Oguri, K. Successive Convexification with Feasibility Guarantee via Augmented Lagrangian for Non-Convex Optimal Control Problems. 2024 ○ This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently proposed successive convexification (SCvx) algorithm by addressing one of its key limitations, that is, the converged solution is not guaranteed to be feasible to the original non-convex problem. The main idea behind the proposed algorithm is to incorporate the SCvx-based iteration into an algorithmic framework based on the augmented Lagrangian method to enable the feasibility guarantee while retaining favorable properties of SCvx. Unlike the original SCvx, this approach iterates on both of the optimization variables and the Lagrange multipliers, which facilitates the feasibility guarantee as well as efficient convergence, in a spirit similar to the alternating direction method of multipliers (ADMM) for large-scale convex programming. Convergence analysis shows the proposed algorithm’s strong global convergence to a feasible local optimum of the original problem and its convergence rate. These theoretical results are demonstrated via numerical examples with comparison against the original SCvx algorithm. • Uzun et al. Successive Convexification for Nonlinear Model Predictive Control with Continuous-Time Constraint Satisfaction. ○ We propose a nonlinear model predictive control (NMPC) framework based on a direct optimal control method that ensures continuous-time constraint satisfaction and accurate evaluation of the running cost, without compromising computational efficiency. We leverage the recently proposed successive convexification framework for trajectory optimization, where: (1) the path constraints and running cost are equivalently reformulated by augmenting the system dynamics, (2) multiple shooting is used for exact discretization, and (3) a convergence-guaranteed sequential convex programming (SCP) algorithm, the prox-linear method, is used to solve the discretized receding-horizon optimal control problems. The resulting NMPC framework is computationally efficient, owing to its support for warm-starting and premature termination of SCP, and its reliance on first-order information only. We demonstrate the effectiveness of the proposed NMPC framework by means of a numerical example with reference-tracking and obstacle avoidance. The implementation is available at https://github.com/UW-ACL/nmpc-ctcs.

2025
• Xie, Z., Chen, X., Wu, J., & Wu, X. (2025). Non-overshooting Fixed Time Control of Free-Flying Space Robotic Manipulators with output constraints: An Inverse Optimal Approach. Aerospace Science and Technology, 161, 110079-. https://doi.org/10.1016/j.ast.2025.110079
    ○ •The virtual controller achieving a practical fixed time convergence of tracking errors shows a non-singular nth derivative with n being any positive integer defined by users. Therefore, the proposed virtual controller shows a higher generality, which could be easily extended to high-order systems.
    ○ •Practical fixed time convergence of tracking errors can be guaranteed, which means a better performance on settling time compared to the works solely achieving UUB or asymptotic stability.
    ○ •The proposed control scheme features a non-overshooting response of tracking errors in the presence of external disturbances and system uncertainties. Moreover, the output constraint can be satisfied at the same time. Thereby, the safety of SRM can be enhanced.
    ○ •Practical inverse optimality of SRM system can be achieved. To the best of author's knowledge, the proposed scheme is the first inverse optimal controller simultaneously achieving practical fixed time convergence, constrained tracking error, and the rigorous non-overshooting response at the presence of uncertainties and disturbances Inverse Optimal Control (IOC) features addressing optimal control problem without the need to solve the complex Hamilton-Jacobi-Bellman (HJB) equation. Although IOC has been extensively studied over the recent years, the state of the art lacks the results of achieving a fixed time non-overshooting response with constrained outputs on IOC schemes. In this paper, an adaptive inverse optimal control scheme is proposed to address the tracking problem of free-flying space robotic manipulators subject to system uncertainties and unknown disturbances, which achieves the practical fixed time non-overshooting response with the constrained tracking errors. More precisely, a novel practical fixed time non-singular virtual controller is designed to define the desired dynamics of tracking errors, which features the non-singular nth derivative where n is any positive integers defined by users. Then, an auxiliary variable is designed to work with the virtual controller to guarantee the absence of overshoot even the system is subject to uncertainties and disturbances. After that, a Fixed Time Disturbance Observer (FTDO) based inverse optimal control scheme is finally constructed to achieve a practical fixed time non-overshooting response with the satisfied output constraints. To the best of author's knowledge, this is the first work of simultaneously achieving non-overshooting response, practical fixed time stability, inverse optimality, and constrained output. The stability of the proposed controller is proven by Lyapunov theory, and the effectiveness is verified by numerical simulations.
• Lishkova & Cannon. A successive convexification approach for robust receding horizon control. IEEE transactions on automatic control, 2025-04,
    ○ A novel robust nonlinear model predictive control strategy is proposed for systems with nonlinear dynamics and convex state and control constraints. Using a sequential convex approximation approach and a difference of convex functions representation, the scheme constructs tubes that contain predicted model trajectories, accounting for approximation errors and disturbances, and guaranteeing constraint satisfaction. An optimal control problem is solved as a sequence of convex programs. We develop the scheme initially in the absence of external disturbances and show that the proposed nominal approach is non-conservative, with the solutions of successive convex programs converging to a locally optimal solution for the original optimal control problem. We extend the approach to the case of additive disturbances using a novel strategy for selecting linearization points. As a result we formulate a robust receding horizon strategy with guarantees of recursive feasibility and closed-loop stability
    
• Successive Convexification for Passively-Safe Spacecraft Rendezvous on Near Rectilinear Halo Orbit