Nonlinear Optimal Control Approach Research Articles

A nonlinear optimal control approach for dual-arm robotic manipulators

A nonlinear optimal control approach for dual-arm robotic manipulators

A nonlinear optimal control approach for 3-DOF four-cable driven parallel robots

In this article, a nonlinear optimal control approach is proposed for the dynamic model of 3-DOF four-cable driven parallel robots (CDPR). To solve the associated nonlinear optimal control problem, the dynamic model of the 3-DOF cable-driven parallel robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the 3-DOF cable-driven parallel robot a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs and a minimum dispersion of energy.

Nonlinear optimal control for triangular tethered multi-satellite formations

Triangular satellite constellations are created by three satellites which are linked through tethers. Such formations serve distributed observation space missions or the creation of high-density satellite communication networks over high-frequency bands. In a tethered multi-satellite system consisting of three-satellites in triangular formation the associated dynamic model exhibits strong nonlinearities. Stabilization and precise positioning of the multi-satellite constellation is a nontrivial task and the solution of the associated nonlinear control problem is an elaborated procedure. In this article a novel nonlinear optimal control method is applied to the above-noted model the tethered multi-satellite system in triangular formation. First, the state-space model of the triangular tethered multi-satellite formation undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the tethered satellites a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and a minimum dispersion of energy when changing the position of the satellites in their triangular tethered formation.

A nonlinear optimal control approach for unmanned surface vessels

A nonlinear optimal control approach for unmanned surface vessels

A robust state-dependent Riccati equation controller with parameter uncertainty and matched disturbance

The state-dependent Riccati equation (SDRE) unveils a nonlinear optimal control approach; the method is sensitive to uncertainty and disturbance that provokes the necessity of precise modeling and omitting disturbance from the model and environment which is occasionally impossible. In this paper, a robust state-dependent Riccati equation is introduced using only the pure SDRE itself. Lyapunov’s second method for stability analysis is used to extract two tuning rules for weighting matrices of the robust approach for handling both matched disturbance and parametric uncertainty. A fourth-order differential equation is simulated to show the effectiveness of the suggested method and the results were compared with conventional SDRE. The robust version could handle the matched disturbance with a steady-state shift from the equilibrium point where the conventional SDRE failed. Additionally, a comparison and detailed analysis have been performed between the proposed design and sliding mode control.

Nonlinear optimal control for permanent magnet synchronous spherical motors

Nonlinear optimal control for permanent magnet synchronous spherical motors

A nonlinear optimal control approach for autonomous reentry space vehicles

Nonlinear control for autonomous reentry space vehicles has been a topic of intensive research during the last years in the area of aerospace science and technology. The associated dynamic model is obtained by expressing position variables and orientation angles of the space vehicle in different coordinate frames, namely an earth-fixed, an earth rotating and a body fixed frame. In this article, a nonlinear optimal control approach is proposed for the dynamic model of reentry space vehicles. It is proven that the longitudinal motion dynamic model of reentry space vehicles is differentially flat and a flatness-based controller is designed about it. Next, in the nonlinear optimal control approach, the dynamic model of the reentry space vehicle undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the reentry space vehicle a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs and a minimum dispersion of energy.

A nonlinear optimal control approach for multi-DOF redundant robotic manipulators

A nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of multi-DOF redundant robotic manipulators. Because of the complicated kinematics and dynamics and the high dimensionality of the state-space model of such robots, the related control problem is of elevated difficulty. In the present article, a three-link planar robotic manipulator it considered. The article’s approach relies first on approximate linearization of the state-space model of the redundant robotic manipulator, according to first-order Taylor series expansion and the computation of the related Jacobian matrices. For the approximately linearized model of the manipulator, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains an algebraic Riccati equation is solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. The proposed control method retains the advantages of typical optimal control, that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.

A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

Nonlinear optimal control for the rotary double inverted pendulum

AbstractThe control problem of the rotary double inverted pendulum (double Furuta pendulum) is nontrivial because of underactuation and strong nonlinearities in the associated state‐space model. The system has three degrees of freedom (one actuated and two unactuated joints) while receiving only one control input. In this article, a novel nonlinear optimal (H‐infinity) control approach is developed for the dynamic model of the rotary double inverted pendulum. First, the dynamic model of the double pendulum undergoes approximate linearization with the use of first‐order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. At a next stage a stabilizing H‐infinity feedback controller is designed. To compute the controller's feedback gains an algebraic Riccati equation has to be solved at each time‐step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. To implement state estimation‐based control without the need to measure the entire state vector of the rotary double‐pendulum the H‐infinity Kalman filter is used as a robust state observer. The nonlinear optimal control method achieves fast and accurate tracking of setpoints by all state variables of the rotary double inverted pendulum under moderate variations of the control input.

An Optimal Control Approach to the Minimum-Time Trajectory Planning of Robotic Manipulators

Trajectory planning is a classic problem in robotics, with different approaches and optimisation objectives documented in the literature. Most of the time, the path is assumed, i.e., pre-defined, and optimisation consists of finding the timing of motion under a number of constraints. The focus of this work is on the minimum-time manoeuvring of robotic manipulators. A nonlinear optimal control approach is proposed that does not require the provision of either a pre-defined path or a pre-defined control structure and allows the inclusion of dynamic constraints. The solution (path and timing of motion) is obtained by transforming the optimal control problem into a nonlinear programming problem. The proposed approach is applied to a two-link manipulator for illustration purposes. The optimisation is carried out both without and with obstacles. The minimum-distance and minimum-time solutions are compared, and some classic results are obtained, including the trapezoidal pattern of the joint velocity and the bang–bang structure of the control torques. The effects of limitations on the jerks of actuators and the rate of change in torque inputs are discussed. The application to a four-link manipulator is also included to show the ‘scalability’ of the approach, together with a comparison with a classic path-and-motion-planning method, to highlight the characteristics and performance of the proposed approach. Finally, the possibility of enforcing a number of via-points along the path is demonstrated. The proposed method allows the computation of the path and motion simultaneously with the computation time, which is 1–30 times the manoeuvre time, on a standard PC with the current implementation.

Nonlinear optimal control for a 4-DOF SCARA robotic manipulator

AbstractSelective compliance articulated robot arms (SCARA) robotic manipulators find wide use in industry. A nonlinear optimal control approach is proposed for the dynamic model of the 4-degrees of freedom (DOF) SCARA robotic manipulator. The dynamic model of the SCARA robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system, a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller’s feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed control method is advantageous because: (i) unlike the popular computed torque method for robotic manipulators, it is characterized by optimality and is also applicable when the number of control inputs is not equal to the robot’s number of DOFs and (ii) it achieves fast and accurate tracking of reference setpoints under minimal energy consumption by the robot’s actuators. The nonlinear optimal controller for the 4-DOF SCARA robot is finally compared against a flatness-based controller implemented in successive loops.

Nonlinear optimal control for a gas compressor driven by an induction motor

The article proposes a nonlinear optimal control approach for the dynamic model of a gas centrifugal compressor being driven by an induction motor (IM). The dynamic model of the integrated compressor-induction motor system, being initially expressed in a nonlinear and multivariable state-space form, undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearized state-space model of the compressor-IM a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem of the compressor-IM under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The global stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control of the compressor-IM, without the need to measure its entire state vector, the H-infinity Kalman Filter is used as a robust state estimator. The differential flatness properties of the compressor-IM system are proven. The article’s method provides one of the few algorithmically simple and computationally efficient solutions for the nonlinear optimal control problem of the compressor-IM system.

A nonlinear optimal control approach for underactuated offshore cranes

ABSTRACT The article proposes a nonlinear optimal control approach for the model of boom cranes being mounted on vessels. The dynamic model of the boom cranes undergoes approximate linearisation with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearised model, an H-infinity feedback controller is designed. The linearisation procedure relies on the computation of the Jacobian matrices of the state-space model of the system. For the computation of the controller's feedback gains, an algebraic Riccati equation is solved at each time step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the boom cranes, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

Trajectory Tracking Design for a Swarm of Autonomous Mobile Robots: A Nonlinear Adaptive Optimal Approach

This research presents a nonlinear adaptive optimal control approach to the trajectory tracking problem of a swarm of autonomous mobile robots. Mathematically, finding an analytical adaptive control solution that meets the H2 performance index for the trajectory tracking problem when controlling a swarm of autonomous mobile robots is an almost impossible task, due to the great complexity and high dimensions of the dynamics. For deriving an analytical adaptive control law for this tracking problem, a particular formulation for the trajectory tracking error dynamics between a swarm of autonomous mobile robots and the desired trajectory is made via a filter link. Based on this prior analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from a high-dimensional nonlinear partial differential equation, which is equivalent to solving the trajectory tracking problem of a swarm of autonomous mobile robots with respect to an H2 performance index. This delivered adaptive nonlinear control solution offers the advantages of a simple control structure and good energy-saving performance. From the trajectory tracking verification, this proposed control approach possesses satisfactory trajectory tracking performance for a swarm of autonomous mobile robots, even under the effects of huge modeling uncertainties.

A Nonlinear Optimal Control Method for Attitude Stabilization of Micro-Satellites

Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites’ state-space model. In this paper, a novel nonlinear optimal (H-infinity) control approach is developed for this control problem. The dynamic model of the satellite’s attitude dynamics undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite’s attitude dynamics. For the approximately linearized description of the satellite’s attitude a stabilizing H-infinity feedback controller is designed. To compute the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis. It is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.

Nonlinear optimal control for the 4-DOF underactuated robotic tower crane

Tower cranes find wide use in construction works, in ports and in several loading and unloading procedures met in industry. A nonlinear optimal control approach is proposed for the dynamic model of the 4-DOF underactuated tower crane. The dynamic model of the robotic crane undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed control approach is advantageous because: (i) unlike the popular computed torque method for robotic manipulators, the new control approach is characterized by optimality and is also applicable when the number of control inputs is not equal to the robot’s number of DOFs, (ii) it achieves fast and accurate tracking of reference setpoints under minimal energy consumption by the robot’s actuators, (iii) unlike the popular Nonlinear Model Predictive Control method, the article’s nonlinear optimal control scheme is of proven global stability and convergence to the optimum.

OpenAP.top: Open Flight Trajectory Optimization for Air Transport and Sustainability Research

Trajectory optimization has been an active area of research for air transport studies for several decades. But almost all flight optimizers proposed in the literature remain close-sourced, which presents a major disadvantage for the advancement of scientific research. This optimization depends on aircraft performance models, emission models, and operational constraints. In this paper, I present a fully open trajectory optimizer, OpenAP.top, which offers researchers easy access to the complex but efficient non-linear optimal control approach. Full flights can be generated without specifying flight phases, and specific flight segments can also be independently created. The optimizer adapts to meteorological conditions and includes conventional fuel and cost index objectives. Based on global warming and temperature potentials, its climate objectives form the basis for climate optimal air transport studies. The optimizer’s performance and uncertainties under different factors like varying mass, cost index, and wind conditions are analyzed. Overall, this new optimizer brings a high performance for optimal trajectory generations by providing four-dimensional and wind-enabled full-phase optimal trajectories in a few seconds.

A nonlinear optimal control approach for the truck and N-trailer robotic system

Truck and N-trailer mobile robots find use in freight transportation, urban transportation, mining as well as in agriculture. The article proposes a nonlinear optimal (H-infinity) control approach for the truck and N-trailer robotic system. The method has been successfully tested so far on the control problem of several types of robotic vehicles and here it is shown that it can also provide an optimal solution to the control problem of the underactuated truck and N-trailer mobile robot. To implement this control scheme, the state-space description of the kinematic model of the truck and N-trailer robotic system undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Next, an optimal (H-infinity) feedback controller is designed. To select the feedback gains of the optimal (H-infinity) controller an algebraic Riccati equation is solved at each time-step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. Finally, to implement state estimation-based feedback control, the H-infinity Kalman Filter is used as a robust state estimator.

A nonlinear optimal control method against the spreading of epidemics

To define a vaccination policy and antiviral treatment against the spreading of viral infections a nonlinear optimal (H-infinity) control approach is proposed. Actually, because of the scarcity of the resources for treating infectious diseases in terms of vaccines, antiviral drugs and other medical facilities, there is need to implement optimal control against the epidemics deployment. In this approach, the state-space model of the epidemics dynamics undergoes first approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization is based on Taylor series expansion and on the computation of the associated Jacobian matrices. Next, an optimal (H-infinity) feedback controller is developed for the approximately linearized model of the epidemics. To compute the controller’s feedback gains an algebraic Riccati equation is solved at each iteration of the control algorithm. Furthermore, the global asymptotic stability properties of the control scheme are proven through Lyapunov stability analysis. This paper’s results confirm that optimal control of the infectious disease dynamics allows for eliminating its spreading while also keeping moderate the consumption of the related medication, that is vaccines and antiviral drugs.