Underactuated Case Research Articles

Realization and Control of Robotic Injection Prototype With Instantaneous Remote Center of Motion Mechanism.

Although there have been studies conducted on the instantaneous remote center of motion (RCM) mechanism, the general closed-loop control method has not been studied. Thus, this article fills that gap and employs the advantages of this mechanism to develop a novel injection system. The injection prototype involves the instantaneous RCM mechanism, insertion unit and injection unit. The RCM system is investigated in the presence of time-varying axial stiffness of the screw drive and underactuated case. For safe interaction, compliance control is designed in the insertion system. The stability of all separate systems is investigated with the bounded parameter variation rate. The injection prototype and a robot end-effector were then combined to perform injection. Our RCM prototype can achieve a large workspace, and its control effectiveness was verified by multiple frameworks and comparison with previous studies. Compliance-controlled insertion can achieve accurate depth regulation and zero-impedance control for manually operating the needle. With the help of three-dimensional reconstruction and hand/eye calibration, the manipulator can guide the injection prototype to a proper pose for injection of a face model. The injection prototype was successfully designed. The effectiveness of the whole control system was verified by simulations and experiments. The particular robotic injection task can be performed by the prototype. This article provides alternative schemes for developing an instantaneous RCM system, screw drive-based surgical tool, and robotic insertion with small needles.

Reduced order in domain control of distributed parameter port-Hamiltonian systems via energy shaping

An in-domain finite dimensional controller for a class of distributed parameter systems on a one-dimensional spatial domain formulated under the port-Hamiltonian framework is presented. Based on (Trenchant et al. 2017) where positive feedback and a late lumping approach is used, we extend the Control by Interconnection method and propose a new energy shaping methodology with an early lumping approach on the distributed spatial domain of the system. Our two main control objectives are to stabilize the closed-loop system, as well as to improve the closed-loop dynamic performances. With the early lumping approach, we investigate two cases of the controller design, the ideal case where each distributed controller acts independently on the spatial domain (fully-actuated), and the more realistic case where the control action is piecewise constant over certain intervals (under-actuated). We then analyze the asymptotic stability of the closed-loop system when the infinite dimensional plant system is connected with the finite dimensional controller. Furthermore we provide simulation results comparing the performance of the fully-actuated case and the under-actuated case with an example of an elastic vibrating string.

Feasibility analysis and saturation control for underactuated spacecraft formation reconfiguration in elliptic orbits

This work proposes a saturation control scheme for underactuated spacecraft formation reconfiguration in elliptic orbits without radial or along-track thrust. Firstly, the rank criterion method is applied to analyze the controllability and feasibility of formation reconfiguration by linearizing the linear time-varying dynamics to linear time-invariant ones. Based on the inherent coupling of the linear time-varying system, the underactuated error dynamics are presented for either underactuated case. Subsequently, the developed underactuated saturation controller can ensure that the time-varying system trajectory asymptotically converges to the specified configuration. The Lyapunov-based analysis presents the constraint conditions of controller parameters and the stable reconfiguration accuracy of the system states. Finally, numerical simulations for both underactuated scenarios are performed in the environment with J2 perturbation to verify the validity of the proposed underactuated control scheme.

Designing an adaptive robust observer for underactuation fault diagnosis of a remote sensing satellite

SummaryThis paper mainly aims at the underactuated case diagnosis due to an actuator failure for a remote sensing satellite. We consider healthy initial conditions for the actuators to investigate the underactuation fault in an attitude tracking control problem. Reaction wheels are the onboard actuators, and a new fault injection mechanism on the speed characteristic is introduced using the multi‐fault function. The fault detection and diagnosis strategy is based on the sliding mode and adaptive sliding mode observers in a finite‐time decision window. The robust observer and adaptive threshold are designed to detect the fault, and the adaptive robust observer estimates the fault model. The residual signal is evaluated by forming the window with fixed thresholds, and in the decision steps, priority is given to the underactuation fault diagnosis. System performance is presented for two actuator fault scenarios in a snapshot imaging mode to understand this case clearly. Numerical simulations close to in‐orbit conditions confirm the satisfactory performance of the proposed strategy that underactuated case is diagnosed by injecting stuck and idle faults around 2.19 and 3.52 s. The times obtained in this study are guaranteed with a 3‐sigma confidence level statistical characteristic. Furthermore, the results of the present work are validated using an air‐bearing experimental test bed to illustrate a more realistic behavior of an underactuated satellite.

Finite-time synchronization control scheme for underactuated satellite formation reconfiguration

A synchronization control scheme for underactuated satellite formation reconfiguration in circular orbits is proposed in this paper. The main idea of the synchronization scheme is to control the satellite without radial or along-track thrust to track its desired configuration while synchronizing its motion with that of other underactuated satellites to maintain the predefined or time-varying formation. Firstly, a new underactuated control approach is presented for either underactuated case. Based on the inherent coupling of the system states, the finite-time convergence of the system trajectory could be guaranteed by the sliding mode-based underactuated controller. Secondly, to synchronize the reconfiguration motion between followers, the sum of the sliding mode errors of every two neighbor followers is defined as the synchronization control. The Lyapunov-based method proves the finite-time convergence of synchronization control. More importantly, the minimum nonzero eigenvalue of the Laplace matrix can reduce the system state convergence region. Numerical simulations also verify the performance of the proposed underactuated synchronization controller.

A Survey on Model-Based Control and Guidance Principles for Autonomous Marine Vehicles

With the increasing number of applications for both surface and underwater autonomous vehicles, a great amount of control methods and guidance principles has been developed over the years. This work proposes a review of the most common of these methods. It is mainly focused on model-based nonlinear control methods and guidance principles. Notably, this work details examples and variations of model-based linearizing controllers, applications of line of sight guidance, sliding mode controllers and several other less common control methods for both fully-actuated and underactuated vehicles. Additionally, this work proposes an alternative definition of underactuation with respect to the task allowing for a better understanding of the consequences of underactuation on control. Comparison of fully-actuated and underactuated cases shows how control laws can be used to solve the problems of underactuation and what mechanisms can be used to compensate for the lack of actuation on a degree of freedom. The reviewed methods are compared and discussed with respect to their capabilities, limitations and suitability for typical tasks.

Intuitive LTI energy-maximising control for multi-degree of freedom wave energy converters: The PeWEC case

Energy-maximising wave energy conversion control strategies are commonly based upon direct optimal control theory, where the control problem is discretised and transcribed into a nonlinear programme, and a solution is found via numerical routines. Though appealing from an optimality viewpoint, the real-time application of such strategies to realistic (complex) wave energy systems, such as the PeWEC device, can become potentially challenging, due to its intrinsic multiple degree-of-freedom (DoF) nature. Furthermore, this pendulum-based system is not only multi-DoF in its nature, but also underactuated, i.e. only one mode, associated to the pendulum mechanism installed inside the wave-excited floating body, can be effectively actuated. We propose, in this paper, a set of four simple and intuitive energy-maximising controllers for the PeWEC system based, upon linear time-invariant (LTI) systems. We achieve this by deriving the so-called impedance-matching conditions for the PeWEC, and extending well-established LTI controllers, originally designed for fully actuated single-DoF systems, to this multi-DoF underactuated case. In particular, we explore, design, and synthesise both feedback, and feedforward configurations, making explicit emphasis in their main characteristics. Furthermore, we provide a performance assessment for each of the proposed controllers, showing their energy-maximising capabilities for the wave resource characterising the Mediterranean Sea.

Indirect Optimization of Underactuated Spacecraft Formation Reconfiguration in Elliptic Orbits

This paper proposes analytical solutions to optimal underactuated spacecraft formation reconfiguration in elliptic orbits, without either the radial or in-track thrust. For either underactuated case, the dynamical model of underactuated formation reconfiguration was developed, based on which the system controllability and reconfiguration feasibility then were analyzed. By using the indirect optimization method, a detailed optimization procedure was designed, and the optimal trajectory of formation reconfiguration was derived analytically for the underactuated cases. A fully actuated optimal reconfiguration scheme was introduced to make comparisons. Numerical simulations indicated that the proposed optimal underactuated reconfiguration schemes can manage formation reconfiguration with a control cost similar to that of the fully actuated scheme, even in the absence of radial or in-track thrust. Numerical comparisons with existing nonoptimal reconfiguration schemes further verified that the proposed optimal schemes can perform underactuated formation reconfiguration in an energy-optimal way.

Exact Task Execution in Highly Under-Actuated Soft Limbs: An Operational Space Based Approach

Recently, the development of soft robots is imposing a change of prospective in several aspects of design and control, moving the robotic field closer to the natural world. Soft robots, like many animals, are often built of continuously deformable elements, and are consequently characterized by a highly under-actuated input space. In this letter we prove that given a generic nonlinear task to be accomplished by a soft robot-as e.g., the positioning of its end effector in space-a linear actuation space with the size of the task itself is already sufficient to achieve the goal. We then introduce the dynamically consistent projector into synergistic space, which can be used to convert controllers designed in operational space, to work in the under-actuated case. This enables a direct translation of control strategies from classic to soft robotics. Leveraging on this result, we present the first dynamic feedback controller for trunk-like soft robots taking in account nonconstant deformations of the soft body. We present simulations showing that using this controller it is possible to track a prescribed dynamic evolution of the robot's tip with zero error at steady state, both in planar and 3-D case with gravity.

Underactuated Stratospheric Airship Trajectory Control Using an Adaptive Integral Backstepping Approach

This paper deals with trajectory tracking control for an underactuated stratospheric airship in the presence of model uncertainties and external disturbances. An adaptive integral backstepping trajectory control is designed from the underactuated airship nonlinear dynamics model. The proposed controller has a two-level structure. A low-level controller based on nonlinear adaptive integral backstepping method stabilizes the attitude and velocity of the airship, whereas a high-level controller performs guidance and trajectory tracking task. Two underactuated cases of zero lateral control force and zero roll moment input are studied. Meanwhile a control allocation component based on active set with weight least square algorithm is put into the low-level controller, to find the optimal control surfaces and thrust inputs under constraints of actuator saturation. By using Lyapunov theory the closed-loop trajectory control system is proven to be globally asymptotically stable. Finally, simulation results show that the proposed adaptive integral backstepping controller can follow the reference even in the presence of parametric uncertainties and external disturbances and time delay inputs.

Attitude control of a picosatellite named NPU-PhoneSat based on shape actuation

This paper investigates the attitude control of a modular picosatellite named NPU-PhoneSat based on shape actuation. The PhoneSat is composed of multiple blocks connected by active joints. Much like a falling cat can reorient itself in mid-air, this modular PhoneSat could reorient itself without changes in net angular momentum by altering the shape and instantaneous mass distribution during attitude maneuvers. Given size and cost constraints, the number of actuators should be limited. Thus, this paper focuses on the under-actuated case. Optimal attitude control method to steer the PhoneSat to the desired posture is proposed in this paper. The inequality constraints are established based on the capacity of the actuator. Particle Swarm Optimization algorithm is employed to search the optimal control input to achieve the reorientation while satisfying the imposed constraints. The input torque is parameterized by the spline to guarantee that initial and final values of control input are zero. Simulation results of zero-angular-momentum reorientation of the PhoneSat are presented which confirm the effectiveness of the proposed method.

Saturated Backstepping Control of Underactuated Spacecraft Hovering for Formation Flights

Based on the inherent coupling of system states, backstepping controllers are designed for underactuated spacecraft hovering without either the radial or in-track thrust and in the presence of input saturation and unmatched disturbances. Feasible hovering positions for either saturated underactuated case are derived. A Lyapunov-based approach is used to prove the asymptotical convergence of state errors and system robustness against unmatched disturbances. The validity of theoretical analysis is verified by simulations in a J2 -perturbed environment.

Dynamics and control of underactuated spacecraft formation reconfiguration in elliptic orbits

Feasibility of underactuated formation reconfiguration in elliptic orbits without radial or in-track thrust is investigated in this paper. For either underactuated case, by using a linear time-varying dynamical model of spacecraft formation, controllability and feasibility analyses are conducted, based on which the preconditions on reconfigurable formations are then derived. With the inherent coupling of system dynamics, the reduced-order sliding mode control technique is employed to design a closed-loop underactuated controller for either case. To ensure the stability of the closed-loop system, the conditions imposed on the controller parameters are derived, and the parameter adaptation laws are then solved analytically. Meanwhile, the explicit relationships between the steady accuracies of system states and the controller parameters are obtained via a Lyapunov-based approach. Numerical examples are simulated in a J2-perturbed environment to validate the theoretical analyses. The results indicate that by using the proposed control schemes, underactuated reconfiguration in elliptic orbits is still feasible even in the absence of radial or in-track thrust and in the presence of unmatched disturbances.

Velocity-free adaptive backstepping control of underactuated spacecraft hovering in circular orbits with input saturation

This paper investigates the output feedback control problem of underactuated spacecraft hovering in circular orbits subject to unmatched disturbances and input saturation. Two underactuated cases without either the radial or in-track thrust are considered. Besides the unavailability of velocity information, the simultaneous loss of velocity measurements and thrust also gives rise to unknown system parameters, a problem not observed in fully-actuated hovering control. To address the lack of velocity measurements, a filter is designed to generate velocity signals. An augmented system is then proposed to deal with the input saturation. By using the inherent coupling of system states, the adaptive backstepping technique is then adopted to estimate the resulting unknown system parameter and design the velocity-free underactuated controller for either case. A Lyapunov-based approach is utilized to prove the stability of the overall closed-loop system, which indicates that all state errors, parameter and velocity estimation errors are asymptotically convergent in the absence of disturbances; and are uniformly ultimately bounded in the presence of disturbances. Finally, numerical simulations are presented to illustrate the performance of the proposed controllers.

Output Feedback Control of Underactuated Spacecraft Hovering in Circular Orbit With Radial or In-Track Controller Failure

This paper proposes the output feedback control schemes for underactuated spacecraft hovering without either the radial or the in-track thrust. In contrast to the conventional fully actuated output feedback hovering control that only lacks velocity signals, a new problem is observed in the underactuated case that the simultaneous loss of velocity measurements and thrust does not only result in the loss of velocity information but also gives rise to unknown system parameters’ effects. Furthermore, due to the loss of thrust, the disturbances turn into unmatched ones. To achieve velocity-free hovering control for the underactuated cases, a novel adaptive reduced-order observer is first proposed for the purpose of velocity and parameter estimation. With the estimates provided by the observer, an output feedback controller is then designed by using the inherent coupling of system states. The asymptotic stability of the overall closed-loop system for either case is guaranteed by a Lyapunov-based method. Finally, numerical simulations are presented to demonstrate the feasibility and validity of the proposed controllers for hovering perturbed by the unmatched disturbances with the simultaneous loss of velocity measurements and thrust.

Fast Terminal Sliding Mode Control of Underactuated Spacecraft Formation Reconfiguration

AbstractFast nonsingular terminal sliding mode controllers (FNTSMCs) are proposed for underactuated spacecraft formation reconfiguration without either the radial or the in-track thrust. A nonlinear dynamic model of underactuated spacecraft formation is developed, which is then linearized about circular reference orbits. Based on the linearized model, the system controllability is analyzed for either underactuated case. Due to the loss of control in a certain direction, the disturbances consisting of the linearization errors and external perturbations do not enter the system from the same channels as those of the control inputs, and therefore turn into unmatched disturbances. To achieve underactuated formation reconfiguration in the presence of unmatched disturbances, underactuated FNTSMCs are designed to indirectly render the system states convergent to the neighborhood of equilibrium by using the inherent coupling of these system states. Modified FNTSMCs are also presented to enhance the system performa...

Collocated Adaptive Control of Underactuated Mechanical Systems

Collocated adaptive control of underactuated mechanical systems is still a concern for the control community. The main difficulty comes from the nonlinearity of the collocated inverse dynamics with respect to the base parameters, which forbids the direct application of classical adaptive control schemes. This paper extends and encompasses the Slotine's adaptive control, which was developed for fully actuated mechanical systems, to stabilize the collocated state space of an underactuated mechanical system. The key point is to define the sliding variable as the difference between the system's velocity and an exogenous state whose dynamics is considered as control input. We first revisit the Slotine's result in view of this definition and then show how to extend it to the underactuated case. Stability and convergence of time-varying reference trajectories for the collocated dynamics are shown to be in the sense of Lyapunov. Global well-posedness of the control laws is achieved by means of a new algebraic property of the mass matrix. Simulations, comparisons to existing control strategies, and experimental results on a two-link manipulator verify the soundness of the proposed approach.

Analytical solutions to optimal underactuated spacecraft formation reconfiguration

Underactuated systems can generally be defined as systems with fewer number of control inputs than that of the degrees of freedom to be controlled. In this paper, analytical solutions to optimal underactuated spacecraft formation reconfiguration without either the radial or the in-track control are derived. By using a linear dynamical model of underactuated spacecraft formation in circular orbits, controllability analysis is conducted for either underactuated case. Indirect optimization methods based on the minimum principle are then introduced to generate analytical solutions to optimal open-loop underactuated reconfiguration problems. Both fixed and free final conditions constraints are considered for either underactuated case and comparisons between these two final conditions indicate that the optimal control strategies with free final conditions require less control efforts than those with the fixed ones. Meanwhile, closed-loop adaptive sliding mode controllers for both underactuated cases are designed to guarantee optimal trajectory tracking in the presence of unmatched external perturbations, linearization errors, and system uncertainties. The adaptation laws are designed via a Lyapunov-based method to ensure the overall stability of the closed-loop system. The explicit expressions of the terminal convergent regions of each system states have also been obtained. Numerical simulations demonstrate the validity and feasibility of the proposed open-loop and closed-loop control schemes for optimal underactuated spacecraft formation reconfiguration in circular orbits.

Modified Transpose Effective Jacobian Law for Control of Underactuated Manipulators

Underactuated manipulators consist of active and passive joints, and developing a control technique that can manage such systems is an attractive, challenging problem. Most works in this area present model-based control laws that require a full dynamics model, and are consequently affected from uncertainties and time delays due to massive computations. Non-model-based control approaches provide an efficient alternative for practical implementation. The Modified Transpose Jacobian (MTJ) algorithm is one of these controllers that has been recently proposed for fully actuated manipulators with a square matrix Jacobian. Based on an approximated feedback linearization approach, the MTJ does not need a priori knowledge of the plant dynamics. In this paper, this scheme is extended to the complicated control problem of underactuated robots in Cartesian space. To this end, the notion of the Transpose Effective Jacobian (TEJ) is presented and so the proposed algorithm is called the Modified TEJ (MTEJ) algorithm. The MTEJ control law employs stored data of the control command in the previous time step, as a learning tool to yield an improved performance. Therefore, the proposed law needs just to a portion of mass matrix that corresponds to passive joint(s), and it is much less affected by inaccuracies in system properties. The gains of the proposed MTEJ can be selected more systematically and do not need to be large; hence, the noise rejection characteristics of the algorithm are improved. Also, no need for the pseudo-inversion of the Jacobian matrix in the proposed controller makes further convenience in the underactuated cases. In addition, the relationship between kinematic and dynamic manipulability measures is discussed for underactuated manipulators. Obtained results show its superior performance even compared to that of the model-based algorithms that need full dynamics models, while the proposed MTEJ requires much lower computation effort.

Neural network-based [formula omitted] control for fully actuated and underactuated cooperative manipulators

This paper develops H ∞ control designs based on neural networks for fully actuated and underactuated cooperative manipulators. The neural networks proposed in this paper only adapt the uncertain dynamics of the robot manipulators. They work as a complement of the nominal model. The H ∞ performance index includes the position errors as well the squeeze force errors between the manipulator end-effectors and the object, which represents a complete disturbance rejection scenario. For the underactuated case, the squeeze force control problem is more difficult to solve due to the loss of some degrees of manipulator actuation. Results obtained from an actual cooperative manipulator, which is able to work as a fully actuated and an underactuated manipulator, are presented.