Explicit Reference Governor Research Articles

Adaptive gain design for Zero-Order Hold discrete-time implementation of explicit reference governor

Explicit reference governor (ERG) is an add-on unit that provides constraint handling capability to pre-stabilized systems. The main idea behind ERG is to manipulate the derivative of the applied reference in continuous time such that the satisfaction of state and input constraints is guaranteed at all times. However, ERG should be practically implemented in discrete-time. This paper studies the discrete-time implementation of ERG, and provides conditions under which the feasibility and convergence properties of the ERG framework are maintained when the updates of the applied reference are performed in discrete time. Specifically, using Zero-Order Hold (ZOH) discretization method, we develop an adaptive algorithm to adjust the gain of the discretized term based on actual measurements to maintain all properties of ERG when implemented in discrete-time. The proposed approach is validated via extensive simulation and experimental studies.

A constrained control framework for unmanned aerial vehicles based on Explicit Reference Governor

This paper tackles the constrained control problem of unmanned aerial vehicles with planar multirotors. The proposed solution splits the constrained control problem into two separate tasks, i.e. stabilization and constraint enforcement. It is shown that the problems addressed by each individual layer is much simpler than the original combined problem. For the unconstrained control of UAVs we consider a control scheme based on a cascade structure. The Lyapunov function for the stabilized cascaded system is then derived. Using this Lyapunov function, we develop an Explicit Reference Governor for constraint enforcement. Numerical simulation shows the effectiveness of the proposed approach.

Tracking control for nonlinear high-order fully actuated system with state constraints: an explicit reference governor approach

This paper studies the tracking control problem of nonlinear high-order fully actuated system subject to state constraints. In order to guarantee the stability of the closed-loop system, a generalised nonlinear proportional differential controller is designed to configure the system into a desired linear constant system. Then, an explicit reference governor for high-order system is introduced to modify the reference signal such that the system state and the state derivatives of certain orders always remain within a prescribed constraint set. Furthermore, we prove that the modified reference will converge to the original reference as much as possible. Therefore, the system state can finally track to the original reference by tracking the modified reference. Two numerical examples demonstrate the validity of the proposed method in this paper.

Experimental validation of a constrained control architecture for a multi-robot bricklayer system

Robotics in construction is an emerging field that aims to automate various construction activities. Among the various innovative technologies for the construction sector, in this paper we focus on robotic solutions for the bricklaying task. In particular, we describe and explain in detail the implementation of a control framework for a recently introduced multi-robot bricklaying concept, specifically designed for laying activities with large and heavy blocks. The multi-robot system subject of this work is based on the collaboration of a robotic manipulator and a crane. The control architecture proposed to perform the construction task belongs to the Explicit Reference Governor (ERG) formalism. The ERG is a constrained control structure that enforces the constraints of the system and ensures that the robotic system operates correctly and safely. The efficiency of the proposed solution is confirmed by experimental validation on a custom-made crane and a KUKA LBR IIWA14R820 robotic arm.

Saturated explicit reference governor for spacecraft constrained attitude reorientation control

In this work, a saturated explicit reference governor (ERG) control scheme is proposed to achieve attitude reorientation maneuver in the presence of pointing constraints and input saturation. Specifically, a saturated controller is first proposed to ensure the asymptotic stability of the closed-loop system. Then, an add-on ERG scheme is designed for guaranteeing constraints satisfactory. A safe trajectory is designed based on the potential functions, and both keep-in and keep-out constraints are enforced by keeping attitudes within the safe invariant sets. Additionally, a hysteresis mechanism is introduced in the manipulation of reference to avoid the unwinding phenomenon. Numerical simulations are included to demonstrate the efficacy and performance of the proposed control strategy.

Real-time constraint-based planning and control of robotic manipulators for safe human–robot collaboration

A recent trend in industrial robotics is to have robotic manipulators working side-by-side with human operators. A challenging aspect of this coexistence is that the robot is required to reliably solve complex path-planning problems in a dynamically changing environment. To ensure the safety of the human operator while simultaneously achieving efficient task realization, this paper introduces a computationally efficient planning and control architecture that combines a Rapidly-exploring Random Tree (RRT) path planner with a trajectory-based Explicit Reference Governor (ERG) by means of a reference selector. The resulting scheme can steer the robot arm to the desired end-effector pose in the presence of actuator saturation, limited joint ranges, speed limits, a cluttered static obstacle environment, and moving human collaborators. The effectiveness of the proposed framework is experimentally validated on the Franka Emika Panda robot arm and fed with feedback information from state-of-the-art depth perception systems. Our method outperforms both the standalone RRT and ERG algorithms in cluttered static environments where it overcomes: i) the RRT’s inability to handle dynamic constraints which result in constraint violations and ii) the ERG’s undesirable property of getting trapped in local minima. Finally we employed the RRT+ERG in highly dynamic human–robot coexistence experiments without sacrificing the real-time requirements.

Asymmetric BLOS constraint-involved intelligent integrated guidance and control approach for flight vehicle equipped with strapdown seeker

The paper investigates the integrated guidance and control (IGC) issue for flight vehicle equipped with strapdown seeker. Distinguished from the routine flight vehicle in literatures, the equipped strapdown seeker is fixedly connected with the vehicle body and thus asymmetric body line of sight (BLOS) constraint is imposed, which makes the IGC design more challenging. Focusing on the point, an intelligent integrated guidance and control approach is proposed by virtue of two specific mechanisms. The improved explicit reference governor technique is adopted to generate auxiliary reference command to ensure asymmetric BLOS limitation not to be violated. On the other hand, the reinforcement learning-based adaptive dynamic programming algorithm is further integrated to guarantee the fine tracking of the auxiliary reference command. Consequently, the satisfactory miss distance is achieved despite of the asymmetric BLOS constraint and unmatched uncertainties, and the stability of the closed-loop system is analyzed. The numerical simulation results demonstrate the effectiveness of the proposed method.

Spacecraft Rendezvous and Docking Using the Explicit Reference Governor Approach

This article investigates the autonomous spacecraft rendezvous and docking problem in the presence of space obstacle, path constraints, and thrust limitation constraint. By introducing the frame of explicit reference governor (ERG), a combination scheme of guidance and control is proposed to guarantee the system stabilization and constraints satisfaction. Specifically, an artificial potential function (APF) method is employed to guide a collision-free trajectory, and then the constraints are satisfied via limiting the states within the safe invariant set. Furthermore, a simplified method is proposed to obtain the maximum bound of the Lyapunov-based invariant sets, which ensures input bounded and collision avoidance. System convergence under the potential field is proved through the Lyapunov stability analysis. Numerical simulation results demonstrate the comprehensive validation and good performance of the proposed method.

Explicit reference governor on [formula omitted] for torque and pointing constraint management

This paper focuses on the constrained attitude control of a rigid body. We propose an Explicit Reference Governor (ERG) specifically designed to handle constraints on SO(3). Two types of constraints are considered: (i) input torque constraints, and (ii) geometric conic pointing constraints. The objective of this paper is to design a control law that is able to steer the attitude of a rigid body to the desired attitude reference while enforcing constraints at all times. To this end, the first step is to design a controller that makes the desired attitude asymptotically stable when constraints (i) and (ii) are neglected. Next, the proposed control scheme is augmented with a novel ERG scheme able to add constraint-handling capabilities to the overall architecture. All the proposed solutions are defined in terms of SO(3) and do not make use of any parameterization such as quaternions or Euler angles. Numerical simulations are carried out to show the effectiveness of the proposed control scheme.

A trajectory-based explicit reference governor for the laying activity with heavy pre-fabricated elements

A trajectory-based explicit reference governor for the laying activity with heavy pre-fabricated elements

Instant distributed MPC with reference governor

Model predictive control is a popular choice for systems that must satisfy prescribed constraints on states and control inputs. Although much progress has been made in distributed model predictive control, existing algorithms tend to be computationally expensive. This limits their use in systems with fast dynamics. In this paper, we propose a new distributed model predictive control algorithm that we term as instant distributed model predictive control (iDMPC). The proposed algorithm employs a realisation of the primal-dual algorithm in the controller dynamics for fast computation. We show that the closed-loop system trajectories with the proposed iDMPC algorithm converge asymptotically to a desired reference. To ensure the satisfaction of the state constraints during the transient, we also include an explicit reference governor in the feedback loop.

An Explicit Reference Governor for Linear Sampled-Data Systems With Disturbance Inputs and Uncertain Time Delays

In this article, we propose a novel reference governor (RG) scheme for prestabilized linear sampled-data systems to satisfy pointwise-in-time constraints in the presence of bounded disturbances and uncertain input and/or measurement delays. Based on an explicit bound on the system response to step changes in the reference signal derived using the logarithmic norm, this RG scheme yields a closed-form solution for updating the reference signal at sample time instants that guarantees both sample-time and intersample constraint satisfaction. Due to its closed-form expression, the proposed RG scheme requires minimum computational effort and is thereby suitable for systems with limited computing capability.

Robust invariance-based explicit reference control for constrained linear systems

In the linear system control, the traditional invariance-based explicit reference governor (ERG) method provides a solution to the control of a class of systems subject to state and control constraints, while there still exist some limitations on the form of system models, which hinders its wider application. In response to this situation, we propose the invariance-based explicit reference control (IERC) which is composed of double-invariance-based explicit reference governor (DIERG) and anti-windup controller (AWC). Specifically, the DIERG forces the system states at the intersection of two invariant sets including the constraint-based invariant set and performance-based invariant set; the AWC adopts amplified artificial amplitudes in control constraints to make the obtained two invariant sets tolerant to some degree of saturation. The advantages of the proposed design methodology are illustrated through the simulation studies.

Safe, Fast, and Efficient Distributed Receding Horizon Constrained Control of Aerial Robot Swarms

This letter proposes a reactive, safe, and high-performance distributed constrained control law for ensuring safety in multi-UAV systems. The UAVs possess higher-order nonlinear dynamics and are subject to actuation and collision avoidance constraints. To address the case of real-time multi-UAV collision avoidance, we propose a novel Trajectory-Tube Distributed Explicit Reference Governor (TT-D-ERG) approach based on the idea of embedding future state trajectories into safety tubes. The control law is ideally suited for systems with limited on-board hardware for computation and communication. The safety, efficacy, performance, and scalability of the method are demonstrated and benchmarked against state-of-the-art real-time collision avoidance methods by simulations and field experiments with multiple quadrotor UAVs (videos at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://youtu.be/V4P1O8vhKlo</uri> ).

Real-time motion control of robotic manipulators for safe human–robot coexistence

This paper introduces a computationally efficient control scheme for safe human–robot interaction. The method relies on the Explicit Reference Governor (ERG) formalism to enforce input and state constraints in real-time, thus ensuring that the robot can safely operate in close proximity to humans. The resulting constrained control method can steer the robot arm to the desired end-effector pose (or a steady-state admissible approximation thereof) in the presence of actuator saturation, limited joint ranges, speed limits, static obstacles, and humans. The effectiveness of the proposed solution is supported by theoretical results and numerous experimental validations on the Franka Emika Panda robotic manipulator , a commercially available collaborative 7-DOF robot arm. • Real-time predictive constrained control with Explicit Reference Governor. • Robotic arm avoids actuator saturations, limited joint and velocity constraints. • Guaranteed robot collision avoidance in static obstacle environments. • Empirical robot collision avoidance in highly dynamic environments. • Safe and performant human–robot coexistence with Franka Emika Panda.

Inverse optimal missile guidance law under constraints based on prescribed-time explicit reference governor

In this paper, the utilization of inverse-optimality-based prescribed-time explicit reference governor is investigated for missile intercepting against unknown maneuvering targets under performance and control input constraints. With an arctangent-based disturbance observer equipped for disturbance elimination, incorporating the inverse optimality approach into the missile interception guarantees the minimization of a performance index. In the framework of prescribed-time explicit reference governor, the control constraint is translated into a restriction of time-varying invariant set, and it follows the prescribed-time regulation of the applied reference along with the restriction satisfaction. The combined prescribed-time explicit reference governor approach could be transformed into a linear matrix inequality optimization problem, and its online solution over a receding horizon gives a Lyapunov function value for reference regulation and then control decisions in the continuous time. Simulation studies are performed to illustrate the performance of the proposed guidance control law.

Explicit reference governor based spacecraft attitude reorientation control with constraints and disturbances

This paper addresses the attitude reorientation problem under the pointing-constraint zone, angular velocity limits, and actuator constraints. The ERG-based control scheme is designed such that the attitude is stabilized, while the state and control constraints stay in the allowable regions defined by the Lyapunov invariant subset. The disturbance observer-based control law is developed in the inner loop of ERG that enables attitude stabilization in the presence of external disturbance. The navigation layer is utilized to manipulate the reference state to enforcing constraints satisfaction. The effectiveness of the proposed constrained attitude control algorithm is then verified through numerical simulations.

Invariant Set Distributed Explicit Reference Governors for Provably Safe On-Board Control of Nano-Quadrotor Swarms

This article provides a theory for provably safe and computationally efficient distributed constrained control, and describes an application to a swarm of nano-quadrotors with limited on-board hardware and subject to multiple state and input constraints. We provide a formal extension of the explicit reference governor framework to address the case of distributed systems. The efficacy, robustness, and scalability of the proposed theory is demonstrated by an extensive experimental validation campaign and a comparative simulation study on single and multiple nano-quadrotors. The control strategy is implemented in real-time on-board palm-sized unmanned erial vehicles, and achieves safe swarm coordination without relying on any offline trajectory computations.

Prescribed‐time control with explicit reference governor for a class of constrained cascaded systems

AbstractDifferent from both finite‐time control (where the settling time depends on the initial condition) and fixed‐time control (whose settling time is subject to an upper bound but varies due to uncertainties and nonlinearities), the prescribed‐time control achieves regulation in prescribed finite time, even under uncertain nonlinearities. This article investigates the prescribed‐time regulation problem for a class of cascaded systems with integral form and control input constraints. The establishment of prescribed‐time property consists of the prescribed‐time regulation controller and prescribed‐time explicit reference governor (PT‐ERG), both of which satisfy the prespecified time requirement. For an elegant implementation, the feasibility for the separate design of controller and governor is guaranteed through a developed prescribed‐time cascaded stable theory. For the prescribed‐time controller, the proposed smooth time‐varying controller provides the prescribed‐time convergence based on a residual‐time‐dependent scaling transformation. For the PT‐ERG dealing with the control input constraints, a reference trajectory with a fixed minimum convergence rate provides an elegant compromise between performance and constraints which keeps the constraint satisfied and tracking errors in an invariant set. Both theoretical analysis and numerical simulations verify the effectiveness of the proposed control scheme.

Reference dependent invariant sets: Sum of squares based computation and applications in constrained control

The goal of this paper is to present a systematic method to compute reference dependent positively invariant sets for systems subject to constraints. To this end, we first characterize these sets as level sets of reference dependent Lyapunov functions. Based on this characterization and using Sum of Squares theory, we provide a polynomial certificate for the existence of such sets. Subsequently, through some algebraic manipulations, we express this certificate in terms of a Semi-Definite Programming problem which maximizes the size of the resulting reference dependent invariant sets. We then present some results implementing the proposed method to an example and propose some variants that may help in reducing possible numerical issues. Finally, the proposed approach is employed in the Model Predictive Control for Tracking scheme to compute the terminal set, and in the Explicit Reference Governor framework to compute the so-called Dynamic Safety Margin. The effectiveness of the proposed method in each of the schemes is demonstrated through simulation studies.