Nonlinear Optimal Control Technique Research Articles

A real-time collision-free maneuver generation algorithm for autonomous driving

In this paper we propose a real-time maneuver generation algorithm for Autonomous Vehicles (AVs). Given a planar road geometry with static and moving obstacles along it, we are interested in finding collision-free maneuvers that satisfied the AV’s dynamics and subject to physical and comfort limits. Based on longitudinal and transverse coordinates, we propose a novel collision avoidance constraint and formulate a suitable maneuver regulation optimal control problem. Maneuver regulation has intrinsic robustness with respect to standard trajectory tracking that stems from the requirement of following a desired path with a desired velocity profile assigned on it. The optimization problem is solved by using a nonlinear optimal control technique that generates (local) optimal trajectories. We demonstrate the efficacy of the proposed algorithm by providing numerical computations on two different scenarios. Finally, experimental results are presented to demonstrate the efficiency of the proposed algorithm both in terms of computational effort and dynamic features captured.

Distilled neural state-dependent Riccati equation feedback controller for dynamic control of a cable-driven continuum robot

This article presents a novel learning-based optimal control approach for dynamic control of continuum robots. Working and interacting with a confined and unstructured environment, nonlinear coupling, and dynamic uncertainty are only some of the difficulties that make developing and implementing a continuum robot controller challenging. Due to the complexity of the control design process, a number of researchers have used simplified kinematics in the controller design. The nonlinear optimal control technique presented here is based on the state-dependent Riccati equation and developed with consideration of the dynamics of the continuum robot. To address the high computational demand of the state-dependent Riccati equation controller, the distilled neural technique is adopted to facilitate the real-time controller implementation. The efficiency of the control scheme with different neural networks is demonstrated using simulation results.

Optimal control applied to TEG harvesting: The necessity of a ring oscillator

In this article, unlike the available literature, an optimal theorem is presented to design conditioning circuits for thermoelectric generator (TEG) energy harvesting without previous ad-hoc assumptions about the electric/electronic structure. The results show that simple linear time-invariant (LTI) conditioning circuits plus an extra non-linear element transforming the TEG's constant voltage into a square wave (ring oscillator) are in fact the optimal choice to pick up the biggest output's energy. This research opens the door to new developments: ring oscillators with ultra-low voltages (less than 1 mV) and non-linear optimal control techniques applied to micro energy harvesting. Real measurement along with LT-Spice simulations is presented to validate the theoretical results, presenting transfer functions for simulation and modeling purposes.

Optimized Intermittent Pharmaceutical Treatment of Cancer Using Non-Linear Optimal Control Techniques

Cancer remains one of the most important diseases and causes of death. In this study, a non-linear mathematical model of tumor growth with immune response, under the effects of chemotherapeutic treatment is studied. Two cost-efficient optimal control approaches are presented based on direct collocation and state dependent Riccati equation methods in order to optimize the pharmaceutical treatment-dosage to the patients. Finally, the numerical results from each method are presented, providing an overall better regimen, when compared to similar previous studies, by successfully eradicating the tumor and minimizing the side-effects of chemotherapy

The effect of Ackermann steering on the performance of race cars

While several papers dealing with the kinematic of mechanisms that approximate the well-known Ackermann steering are available, apparently there are no contributions related to the effect of Ackermann steering on vehicle performance. This work focuses on the effect of Ackermann steering and parallel steering on the performance of a racing car, after a discussion on the different definitions of Ackermann steering ratio available in the literature. Three scenarios are considered: steady turning, slalom and a circuit lap. Nonlinear optimal control techniques are employed to assess the maximum performance. A Formula SAE car model is used and validated against experimental data in acceleration, steady turning and slalom. Then the same model is employed to investigate the effect of different steering layouts.

Finite Horizon Optimal Nonlinear Spacecraft Attitude Control

This research is devoted to present spacecraft attitude control via a finite-horizon nonlinear optimal control technique. The spacecraft kinematics are represented using the modified Rodrigues parameters, which possess singularities for eigenaxis rotations greater than 180 degree. The proposed technique is based on State Dependent Riccati Equation (SDRE). In this technique, the differential Riccati equation is converted to a linear Lyapunov differential equation. This technique can be applied for finite-horizon nonlinear regulation and tracking problems. The proposed technique is effective for a wide range of operating points. Simulation results are given to illustrate the effectiveness of the finite horizon technique.

Indirect robust suboptimal control of two-satellite electromagnetic formation reconfiguration with geomagnetic effect

As a novel approach to control the relative motion of a satellite formation, electromagnetic formation flight (EMFF) has some prominent advantages, such as no propellant consumption and no plume contamination, and has a broad prospect of application in such fields as on-orbit detection and optical interferometry. The current paper investigates the optimal control for the reconfiguration of a two-satellite electromagnetic formation using the nonlinear quadratic optimal control technique. Specifically, the effects of the Earth’s magnetic field on the EMFF satellites are analyzed, and then the nonlinear translational dynamic model of a two-satellite electromagnetic formation is derived by utilizing the analytical mechanics theory. Considering the high nonlinearity and coupling in the dynamic model and the actuator saturation, a closed-loop robust suboptimal control strategy based on the indirect robust control scheme and the θ-D technique is proposed with robust stability and optimality. To ensure a further reduction of control input, the designed suboptimal controller is modified by applying the Tracking-Differentiator. The feasibility of the derived translational dynamics and proposed control strategy for the robust reconfiguration mission is validated through theoretical analysis and numerical simulations.

A Methodology for Applying Conditional Nonlinear Optimal Perturbation and Natural Cybernetics to Tropical Cyclone Mitigation

Investigations into tropical cyclone mitigation, especially those made by Ross Hoffman, are introduced in the beginning to elicit the weather control version of 4-Dimensional Variation (4D-Var) as a nonlinear optimal control technique and the theory of natural cybernetics. Subsequently, the concept of Conditional Nonlinear Optimal Perturbations (CNOP) and the existing connotation of natural cybernetics related to weather modification are briefly presented. After that, the primary application of CNOP, improved by comparison with 4D-Var, are stressed upon, which can make use of the observational data during the controlling process, thereby having some advantages over 4D-Var in weather control. The technique may be called ‘nonlinear optimal forcing variation calculus (NOFV)’ or ‘nonlinear optimal forcing perturbation (NOFP)’ approach, which could make controlling as close to the observation as possible. Moreover, two other applications of CNOP, i.e. inversion of the initial perturbation evolving into a tropical cyclone and the solution of perturbation yielding maximum vertical wind shear with CNOP, are further investigated. Subsequently, the application of natural cybernetics to tropical cyclone mitigation and control, is analyzed in comparison with precipitation enhancement. Meanwhile, the means to realize tropical cyclone control and mitigation are synoptically reviewed. The investigation and analysis show that CNOP approach and natural cybernetics are useful in tropical cyclone mitigation and control.

Nonlinear Optimal Control of Relative Rotational and Translational Motion of Spacecraft Rendezvous

AbstractA nonlinear optimal control technique is utilized to address coupled relative rotational and translational motion in spacecraft rendezvous. A new formulation of relative rotational dynamic ...

An Efficient Minimum-Time Trajectory Generation Strategy for Two-Track Car Vehicles

In this paper, we propose a novel approach to compute minimum-time trajectories for a two-track car model, including tires and (quasi-static) longitudinal and lateral load transfer. Given the car model and a planar track, including lane boundaries, our goal is to find a trajectory of the car minimizing the traveling time subject to steering and tire limits. Moreover, we enforce normal force constraints to avoid wheel liftoff. Based on a projection operator nonlinear optimal control technique, we propose a minimum-time trajectory generation strategy to compute the fastest car trajectory. Numerical computations are presented on two testing scenarios, a 90° turn and a real testing track. The computations allow us to both demonstrate the efficiency and accuracy of the proposed approach and highlight important features of the minimum-time trajectories. Finally, we integrate our strategy into a commercial vehicle dynamics software, thus computing minimum-time trajectories for a complex multibody vehicle model. The matching between the predicted trajectory and the one of the commercial toolbox further highlights the effectiveness of the proposed methodology.

Optimal Control Based Dynamics Exploration of a Rigid Car With Longitudinal Load Transfer

In this brief, we provide optimal control-based strategies to explore the dynamic capabilities of a single-track car model that includes tire models and longitudinal load transfer. First, we propose numerical tools to analyze the equilibrium manifold of the vehicle. That is, we design a continuation and predictor-corrector numerical strategy to compute the cornering equilibria on the entire range of operation of the tires. Second, as a main contribution of this brief, we explore the system dynamics by the use of nonlinear optimal control techniques. Specifically, we propose a combined optimal control and continuation strategy to compute aggressive car trajectories. To show the effectiveness of the proposed strategy, we compute aggressive maneuvers of the vehicle inspired to testing maneuvers from virtual and real prototyping.

The Optimality of the Handbrake Cornering Technique

The paper investigates the optimality of the handbrake cornering, a strategy widespread among rally drivers. Nonlinear optimal control techniques are used to mimic real driver behavior. A proper yet simple cost function is devised to induce the virtual optimal driver to control the car at its physical limits while using the handbrake technique. The optimal solution is validated against experimental data by a professional rally driver performing the handbrake technique on a loose off-road surface. The effects of road surface, inertial properties, center of mass position, and friction coefficient are analyzed to highlight that the optimality of the maneuver does not depend on the particular vehicle data set used. It turns out that the handbrake maneuvering corresponds to the minimum time and minimum (lateral) space strategy on a tight hairpin corner. The results contribute to the understanding of one of the so-called aggressive driving techniques.

An Approach to Explicate the Dexterity of Driving by Nonlinear Optimal Control Technique

An Approach to Explicate the Dexterity of Driving by Nonlinear Optimal Control Technique

Minimum time cornering: the effect of road surface and car transmission layout

This paper investigates the minimum time/limit handling car manoeuvring through nonlinear optimal control techniques. The resulting ‘optimal driver’ controls the car at its physical limits. The focus is on cornering: different road surfaces (dry and wet paved road, dirt and gravel off-road) and transmission layouts (rear-wheel-drive, front-wheel-drive and all-wheel-drive) are considered. Low-drift paved circuit-like manoeuvres and aggressive/high-drift even counter-steering rally like manoeuvres are found depending on terrain/layout combinations. The results shed a light on the optimality of limit handling techniques.

Neural Network-Based Optimal Control of Mobile Robot Formations With Reduced Information Exchange

A novel formation control scheme for mobile robots is introduced in the context of leader-follower framework with reduced communication exchange. The dynamical controller inputs for the robots are approximated from nonlinear optimal control techniques in order to track the designed control velocities generated by the kinematic controller. The proposed nonlinear optimal control technique, referred to as adaptive dynamic programming, uses neural networks (NNs) to solve the optimal formation control problem in discrete time in the presence of unknown internal dynamics and a known control coefficient matrix. A modification to the follower's kinematic controller is used to allow the desired formation to change in order to navigate around obstacles. The proposed obstacle avoidance technique modifies the desired separation and bearing of the follower to guide the follower around obstacles. Minimal wireless communication is utilized between the leader and the follower to allow the follower to approximate and compensate for the formation dynamics. All NNs are tuned online, and the stability of the entire formation is demonstrated using Lyapunov methods. Hardware results demonstrate the effectiveness of our approach.

Optimal Reconfigurations of Two-Craft Coulomb Formation in Circular Orbits

Optimal reconfigurations of a two-spacecraft Coulomb formation are determined by applying nonlinear optimal control techniques. The objective of these reconfigurations is to maneuver the two-craft formation between two charged equilibria configurations. The four optimality criteria considered are minimum time, minimum acceleration of the separation distance, minimum Coulomb and electric propulsion fuel usage, and minimum electrical power consumption. The reconfiguration between equilibra is first considered by varying the desired separation distance. In a radial relative equilibrium configuration, only the Coulomb force is required to control the in-plane motion and to steer the satellites from their initial to their final radial position. In this reconfiguration maneuver, the gravity gradient torque is exploited to stabilize the in-plane motion. For along-track and orbit normal equilibrium locations, the reconfiguration maneuver requires hybrid controls. Here the Coulomb force is varied to control the separation distance and inertial micro-thrusters are activated for control in the transverse directions. Second, a reconfiguration involving hybrid control is used to maneuver the crafts from any initial equilibrium position to a final one. The goal is to determine optimal maneuvers maximizing the use of Coulomb propulsion while minimizing the electric propulsion usage. The two-point boundary value problem optimization formulation is numerically solved via pseudo-spectral methods. Pontryagin’s Minimum Principle verifies the open loop solutions’ optimality.

Energy optimal spacecraft attitude control subject to convergence rate constraints

Attitude control of operational satellites is still predominantly performed by standard controllers such as Proportional plus Derivative (PD) control laws, which are still preferred for implementation to the computationally intensive nonlinear optimal control techniques, representing higher implementation complexity. In this paper, an inverse optimal control approach based on phase space geometry is presented, which is easy to implement and free from numerical and computational issues. The optimal control objective is to minimize a norm of the control torque subject to a rapidity constraint on the convergence rate of a Lyapunov function, under the effect of a benchmark controller. The proposed optimization method is shown to significantly enhance the torque-rapidity trade-off compared to the benchmark controller, chosen to be a PD law then a sliding mode controller. The inverse optimal control scheme is implemented on an air bearing table experimental platform.

DISCRETE-TIME OPTIMAL CONTROL OF NONHOLONOMIC MOBILE ROBOT FORMATIONS USING LINEARLY PARAMETERIZED NEURAL NETWORKS

In this paper, the infinite horizon optimal tracking control problem is solved online and forward-in-time for leader follower based formation control of nonholonomic mobile robots. Using the back-stepping approach and the kinematic controller developed in our previous work, the dynamical controller inputs for the robots are approximated from nonlinear optimal control techniques to track the designed control velocities. The proposed adaptive dynamic programming approach uses neural networks (NNs) to solve the optimal formation control problem in discrete-time in the presence of unknown internal dynamics and a known control coefficient matrix. All NNs are tuned online using novel weight update laws, and the stability of the entire formation is demonstrated using Lyapunov methods. Numerical simulations are also provided to demonstrate the effectiveness of the proposed approach.

Nonlinear optimal control of spacecraft approaching a tumbling target

This paper investigates the control of spacecraft to approach to and align with a tumbling target. The potential application is to perform on-orbit autonomous satellite servicing. In order to complete the task, the spacecraft is required to perform large position and attitude maneuvers with sufficient accuracy. In addition, the flexible motion induced by large angular maneuvers needs to be minimized. The primary contribution of this work is to consider the control of position and attitude of rigid body and suppression of flexural deformation in one optimal control framework. The 6-DOF rigid body dynamics and coupled flexible structure dynamics are highly nonlinear and lead to a challenging control problem. The θ – D nonlinear optimal control technique is employed to design a closed-form feedback controller for this problem by finding an approximate solution to the Hamilton–Jacobi–Bellman (HJB) equation through a perturbation process. The closed-form controller offered by this approach is easy to implement onboard especially for this problem with a large state-space. Numerical results show that the proposed controller exhibits good tracking performance even under large moment of inertia uncertainties.

Integrated nonlinear optimal control of spacecraft in proximity operations

This article proposes an integrated optimal control strategy for a servicing spacecraft in proximity operations on a target in space. The relative position vector between the servicing spacecraft and the target is required to direct towards the docking port of the target while the attitude of the two bodies must be synchronised without exciting large flexible vibrations. The control of translational, rotational and flexible motions is formulated in one unified optimal control framework in which the tracking errors in relative position and attitude, and flexible structure vibrations can be minimised simultaneously using one cost function. This formulation results in a highly nonlinear system that poses a challenging control problem. The nonlinear optimal control technique is employed to design a closed-form feedback control law for this nonlinear control problem by finding an approximate solution to the Hamilton–Jacobi–Bellman (HJB) equation through a perturbation process. The closed-form controller offered by this approach is easy to implement onboard especially for this problem with a large state-space. Numerical simulations including the six degrees-of-freedom rigid body dynamics and coupled flexible structure dynamics are performed to demonstrate the effectiveness of this control formulation even under large moment of inertia uncertainties.