3D environmental extremum seeking navigation of a nonholonomic mobile robot

A nonholonomic under-actuated robot with bounded control travels in a 3D region. A single sensor provides the value of an unknown scalar field at the current location of the robot. We present a new kinematic control paradigm to drive the robot to the maximizer of the field, which is different from conventionally trying to align the velocity vector with the field gradient. The proposed strategy does not employ gradient estimation and is non-demanding with respect to both computation and motion. Its mathematically rigorous analysis and justification are provided. Simulation results confirm the applicability and performance of the proposed guidance approach.     

An extremum seeking approach via variable-structure control for fed-batch bioreactors with uncertain growth rate

In this paper, we present an extremum-seeking scheme based on an approach to variable structure control for fed-batch bioreactors. The proposed scheme deals with uncertainty on the specific growth rate without assuming an explicit mathematical expression. The control approach exploits the inhibitory effect of the substrate concentration on the growth rate, in such a manner that the closed-loop system reaches the sliding regime on an optimal switching manifold, which is defined by maximizing biomass production. The control scheme comprises an estimation scheme consisting of a high-gain observer and a discrete gradient estimator which computes the unknown terms. The practical stabilizability for the closed-loop system around an unknown optimal set-point is analyzed. Numerical experiments illustrate the effectiveness of the proposed approach.     

极值搜索控制系统的一体化设计研究

针对传统极值搜索控制系统设计中,极值搜索算法与控制器采取单独设计易导致系统难以发挥其最佳性能的问题,提出一套极值搜索控制系统的一体化设计方法.此方法充分考虑到系统的非线性和不确定性,建立了极值搜索算法与被控对象的一体化设计模型,运用终端滑模切换面和相应的控制策略,使极值搜索算法在较短时间内搜寻到系统的最优值,而且其输出值可很快收敛至此最优值.理论分析和仿真结果分别验证了此方法的稳定性和有效性.     

Extremum seeking with sliding mode gradient estimation and asymptotic regulation for a class of nonlinear systems

This paper presents a model-based extremum seeking approach for a class of single-input–single-output nonlinear systems, with the analytic form of the performance function unknown a priori. We focus on a practically implementable design with robustness to model uncertainties and disturbances. A discrete-time sliding mode gradient estimator is developed for estimating the gradient of the performance profile. Based on the estimate, a variable structure output feedback regulator is proposed to enforce the system states toward the optimal trajectory. We analyze convergence conditions of the switching system toward a neighborhood of the optimal trajectory, and establish an ultimate bound on the size of the neighborhood. The robustness of the proposed controller is discussed with respect to measurement noise.     

Navigation with constraints for an autonomous mobile robot

This paper describes a navigation planning algorithm for a robot capable of autonomous navigation in a structured, partially known and dynamic environment. This algorithm is applied to a discrete workspace composed of a network of places and roads. The environment specification associates temporal constraints with any element of the network, and recharge or relocalisation possibilities with places. A mission specification associates several constraints with each navigation task (energy, time, position uncertainty and distance).

The algorithm computes an optimal path for each navigation task according to the optimization criterion and constraints. We introduce the notion of efficient path applied to a new best first search algorithm solving a multiple constraints problem. The path determination relies on a state representation adapted to deal with environment constraints. We then prove that the complexity chracteristics of our algorithm are similar to those of the A* algorithm.

The planner described in this paper has been implemented on a Spare station for a Robuter mobile platform equipped with ultra-sonic range sensors and an active stereo vision system. It was developed for the MITHRA family of autonomous surveillance robots as part of project EUREKA EU 110.     

Range-only measurements based target following for wheeled mobile robots

We consider the problem of navigation and guidance of a wheeled mobile robot towards a maneuvering target based on the measurements concerning only the distance from the robot to the target. We propose a sliding mode controller that drives the robot to the predefined distance from the target and makes the robot follow the target at this distance. Mathematically rigorous proof of convergence and stability of the proposed guidance law is presented. Simulation results confirm the applicability and performance of the proposed guidance approach.     

On global extremum seeking in the presence of local extrema

We propose a global extremum seeking scheme which can seek the global optimal value in the presence of local extrema. It is shown that the proposed global extremum seeking scheme can converge to an arbitrarily small neighborhood of the global extremum from an arbitrarily large set of initial conditions if sufficient conditions are satisfied. A simple example illustrates the effectiveness of the proposed scheme.     

On-line optimization of fedbatch bioreactors by adaptive extremum seeking control

In this paper, we present an adaptive extremum seeking control scheme for fed-batch bioreactors with Haldane kinetics. The proposed adaptive extremum seeking approach utilizes the structure information of the process kinetics to derive a seeking algorithm that drives the system states to the desired setpoints that maximize the biomass production. It assumes that only the substrate concentration is available for on-line measurement. Lyapunov stability is used in the design of the extremum seeking controller structure and the development of the parameter learning laws. The performance of the approach is illustrated via numerical simulations.     

四旋翼无人机自适应导航控制

研究四旋翼(Quadrotor)无人机导航控制问题。针对传统的四旋翼无人机导航控制方法的目标定位误差和实时性差问题,提出了基于CLOS技术的导航控制方法。采用CLOS技术所开发的导航控制系统使得四旋翼无人机能够在移动停机坪完成自主导航和着陆的任务,并详细研究了导航控制系统的设计和仿真。仿真结果显示了所设计的导航控制系统的性能和有效性,可应用于四旋翼无人机的实时导航。     

On non-local stability properties of extremum seeking control

In this paper, we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted. This non-local stability result is proved by showing semi-global practical stability of the closed-loop system with respect to the design parameters. We show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction. Our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking. Simulation examples illustrate our results.     

Combining extremum seeking control and tracking control for high-performance CVT operation

The design of a new controller for the variator in a pushbelt continuously variable transmission (CVT) is investigated. A conventional variator controller is typically based on a variator model with large uncertainties, which results in a limited variator efficiency. The proposed controller simultaneously optimizes the variator efficiency and tracks a transmission ratio reference, for which a detailed variator model is not required. The controller, a combination of extremum seeking control and tracking control, only uses measurements from standard sensors. Experiments on the basis of a driving cycle show that a conventional variator controller is outperformed.     

Robust and adaptive design of numerical optimization-based extremum seeking control

We consider the employment of numerical optimization and state regulation to solve the extremum seeking control (ESC) problem, which does not assume the time scale separation between the plant dynamics and the extremum seeking loop. Extremum seeking is realized via a state regulator that drives the state traveling along a convergent set point sequence generated by a numerical optimization algorithm. In this paper, we propose a novel design of an asymptotic state regulator via output tracking for state feedback linearizable systems, where we trade off finite time state regulation to obtain flexibility in designing a robust extremum seeking controller. Existing techniques such as nonlinear damping and nonlinear adaptive control are then used to deal with input disturbance and unmodeled plant dynamics. Simulation examples illustrate the effectiveness of the basic and robust extremum seeking schemes, and some design guidelines are provided for engineering applications.     

Output feedback adaptive extremum seeking control of a continuous stirred tank bioreactor with Monod's kinetics

An adaptive extremum seeking controller is presented for the optimization of the production rate of a continuous stirred tank bioreactor with Monod's kinetics. This controller is saturated outside a domain of interest and a reduced-order observer is designed to estimate the substrate concentration in the bioreactor. It is shown that once a persistence of excitation condition is satisfied, the convergence of the parameter estimates to their true values is guaranteed. Semi-global asymptotic stability for the output feedback closed-loop system is proved based on Lyapunov's theorem. Simulation results are shown to illustrate the performance of the proposed approach.     

On the choice of dither in extremum seeking systems: A case study

We discuss how the choice of dither (excitation signal) affects the performance of extremum seeking using a benchmark situation: a static scalar map; and a simple scalar extremum seeking scheme. Our comparisons are based on the performance of the system with different dithers in terms of three performance indicators: the speed of convergence, domain of attraction and accuracy (i.e. the ultimate bound on trajectories). Our analysis explicitly shows how the dither shape affects each of these performance indicators. Our study suggests that the practitioners using extremum seeking control should consider the dither shape as an important design parameter. Computer simulations support our theoretical findings.     

Unified frameworks for sampled-data extremum seeking control: Global optimisation and multi-unit systems

Two frameworks are proposed for extremum seeking of general nonlinear plants based on a sampled-data control law, within which a broad class of nonlinear programming methods is accommodated. It is established that under some generic assumptions, semi-global practical convergence to a global extremum can be achieved. In the case where the extremum seeking algorithm satisfies a stronger asymptotic stability property, the converging sequence is also shown to be stable using a trajectory-based proof, as opposed to a Lyapunov-function-type approach. The former is more straightforward and insightful. This allows for more general optimisation algorithms than considered in existing literature, such as those which do not admit a state-update realisation and/or Lyapunov functions. Lying at the heart of the analysis throughout is robustness of the optimisation algorithms to additive perturbations of the objective function. Multi-unit extremum seeking is also investigated with the objective of accelerating the speed of convergence.     

Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties

We pose and solve an extremum seeking control problem for a class of nonlinear systems with unknown parameters. Extremum seeking controllers are developed to drive system states to the desired set-points that extremize the value of an objective function. The proposed adaptive extremum seeking controller is “inverse optimal” in the sense that it minimizes a meaningful cost function that incorporates penalty on both the performance error and control action. Simulation studies are provided to verify the effectiveness of the proposed approach.     

Online optimization of spark advance in alternative fueled engines using extremum seeking control

Alternative fueled engines offer greater challenges for engine control courtesy of uncertain fuel composition. This makes optimal tuning of input parameters like spark advance extremely difficult in most existing ECU architectures. This paper proposes the use of grey-box extremum seeking techniques to provide real-time optimization of the spark advance in alternative fueled engines. Since practical implementation of grey-box extremum seeking methods is typically done using digital technology, this paper takes advantage of emulation design methods to port the existing continuous-time grey-box extremum seeking methods to discrete-time frameworks. The ability and flexibility of the proposed discrete-time framework is demonstrated through simulations and in practical situation using a natural gas fueled engine.     

Observer-based perturbation extremum seeking control with input constraints for direct-contact membrane distillation process

An observer-based perturbation extremum seeking control is proposed for a direct-contact membrane distillation (DCMD) process. The process is described with a dynamic model that is based on a 2D advection-diffusion equation model which has pump flow rates as process inputs. The objective of the controller is to optimise the trade-off between the permeate mass flux and the energy consumption by the pumps inside the process. Cases of single and multiple control inputs are considered through the use of only the feed pump flow rate or both the feed and the permeate pump flow rates. A nonlinear Lyapunov-based observer is designed to provide an estimation for the temperature distribution all over the designated domain of the DCMD process. Moreover, control inputs are constrained with an anti-windup technique to be within feasible and physical ranges. Performance of the proposed structure is analysed, and simulations based on real DCMD process parameters for each control input are provided.     

Development of a stair-climbing mobile robot with legs and wheels

This paper deals with the development of a stair-climbing mobile robot with legs and wheels. The main technical issues in developing this type of robot are the stability and speed of the robot while climbing stairs. The robot has two wheels in the front of the body to support its weight when it moves on flat terrain, and it also has arms between the wheels to hook onto the tread of stairs. There are two pairs of legs in the rear of the body. Using not only the rorational torque of the arms and the wheels, but also the force of the legs, the robot goes up and down stairs. It measures the size of stairs when going up and down the first step, and therefore the measurement process does not cause this robot to lose any time. The computer which controls the motion of the robot needs no complicated calculations as other legged robots do. The mechanism of this robot and the control algorithm are described in this paper. This robot will be developed as a wheelchair with a stair climbing mechanism for disabled and elderly people in the near future. This work was presented, in part, at the International Symposium on Artificial Life and Robotics, Oita, Japan, February 18–20, 1996     

Robust trajectories following control of a 2-link robot manipulator via coordinate transformation for manufacturing applications

A common idea concerning trajectory control of robot manipulators is to tackle the motion of the end-effector. According to traditional trajectory designs, a prescribed profile in a work space is first decomposed into independent joint positions such that the success in a contouring task lies with good tracking capability of individual joints. To advance trajectory control precision without relying on high tracking performance, a contour control strategy for a robot manipulator is presented in this paper. Different from the traditional concept of trajectory control, a contour following control strategy is developed via a coordinate transformation scheme. The main advantage of the proposed control architecture is that the final contouring accuracy will not be degraded in case the tracking performance of the robot manipulator is not good enough. Moreover, using a concept of variable structure control theory, a smooth robust control algorithm is realized in the form of proportional control plus an integration term. The robustness of the control algorithm is also demonstrated. A number of experiments are conducted to demonstrate the advantage of the trajectories following control framework and validate the feasibility of the proposed controller.