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An adaptive production control structure for failure-prone manufacturing systems under inventory and demand uncertainty is proposed. It contains estimation and forecasting modules incorporated into a control loop. The customer demand is unknown and its rate is composed of ramp-type, seasonal and random components. Information available to decision maker consists of imprecise inventory records, and the Kalman filter technique is used for estimating the inventory level and demand rate online from noisy inventory measurements. Estimates obtained are shown to converge to the actual values in stochastic sense. They are subsequently used for demand component forecasting, once the estimation errors become sufficiently small. A forecasting algorithm allows estimating ramp-type and seasonal demand components, together with their potential errors. Obtained estimates are incorporated into production control procedures, recently developed for manufacturing systems under variable and uncertain demand. Optimality conditions in the form of Hamilton-Jacobi-Bellman equations are obtained. A constructive numerical method for computing sub-optimal production policies is proposed and validated through numerical simulations.

We consider a hybrid manufacturing–remanufacturing system that consists of a flexible machine capable of sharing its production time between manufacturing mode in which raw materials are used in production process and remanufacturing mode in which returned products are used instead. The machine is supposed to be failure-prone and subject to age-dependent deterioration. Returned products vary significantly in type and quality due to different collection and recovery procedures. This variability often adversely affects machine operation in remanufacturing mode. To investigate the role of this factor within deterioration/maintenance framework, we suppose that machine's age-dynamics depends mainly on the remanufacturing intensity. This deterioration is characterized by the increasing failure rate and thus leads to the loss of machine availability. Preventive maintenance is used to recover the machine availability. Combined optimization of manufacturing, remanufacturing and maintenance policies is considered. It aims at minimizing the total cost that comprises manufacturing, remanufacturing, maintenance, inventory and backlog costs. This problem for flexible hybrid manufacturing–remanufacturing deteriorating systems was rarely considered in the literature. The problem is addressed using stochastic dynamic programming approach, leading to numerical solution of Hamilton-Jacobi-Bellman equations. Feasibility conditions for age-deteriorating systems are developed. Numerical examples and sensitivity analysis are used to determine the key characteristics of the system and to describe the system behaviors under optimal strategies.

Failure-prone manufacturing systems facing dynamical market conditions that result in demand variations are considered. The combined production and corrective maintenance optimization problem for a one-machine-one-product system is addressed. Repairing the machine after the failure, the manager has to solve the dilemma: to choose an inexpensive (but lower) repair rate, or to use the higher, (but more expensive) repair rate. The former decision seems to be appropriate when there is no risk of inventory shortage, while the latter one has to be used in critical (stock shortage) situations. Precise solution to this problem presented in the paper is theoretically instructive and valuable for practitioners. Optimality conditions in the form of time-dependent Hamilton–Jacoby–Bellman equations are obtained and a novel numerical approach is proposed for solving these equations for the case of periodically time-varying demand. The optimal policy is shown to be the hedging-curve-policy, that extends the hedging-point-policy to the case of varying level of safety stock. The simulation results show that the optimal policies have an important property of anticipating the future demand evolutions and making the optimal decisions relevant to such dynamic conditions. In particular, it has been shown that in the large domain of the system parameters it is advantageous to use the lower (and inexpensive) repair rate when the stock is approaching the hedging level and especially when the demand level is near its bottom edge.

PurposeThe purpose of this paper is to find the optimal production and setup policies for a manufacturing system that produces two different types of parts. The manufacturing system consists of one machine subject to random failures and repairs. Reconfiguring the machine to switch production from one type of product to another generates a non-production time and a significant cost.Design/methodology/approachThis paper proposes an approach based on the development of optimal production and setup policies, taking into account the possibilities of undertaking the setup for all modes of the machine, and covering them at the end of setup. New optimality conditions are developed in terms of modified Hamilton-Jacobi-Bellman (HJB) equations and recursive numerical methods are applied to solve such equations.FindingsThe proposed approach led to determine more realistic production rates of both parts and setup sequences for the different modes of the machine that significantly influence the inventory and the system capacity. A numerical example and sensitivity analysis are used to determine the structure of the optimal policies and to show the helpfulness and robustness of the results obtained.Practical implicationsFollowing the steps of the proposed approach will provide the control policies for industrial manufacturing systems with setup permitted at all modes of the machine, and when the setup does not necessarily restore the machine to its operational mode. The proposed optimal policy takes into account the stochastic nature of the machine mode at the end of setup and we show that ignoring it leads to non-natural policies and underestimates significantly the safety stock thresholds.Originality/valueConsidering the assumptions presented in this paper leads to a new structure of the control laws for the production planning of manufacturing systems with setup.

Reliable quantitative description of the manufacturing process is indispensable for supporting the effective management of the company within current industrial reality. Time estimation is an important element of the effort evaluation process which is essential along many phases of business development from bidding for competitive contracts to design and production phases. In particular, the time estimates are useful in the resource planning process, especially when the precision of the provided estimates can be quantitatively characterized. We propose in this work an approach that combines the techniques developed within predetermined time methods (such as MODAPTS and MINIMOST) with the statistical techniques that use the real data (collected along the stop-watch time measurements). Our approach allows to obtain not only time estimates themselves, but also the confidence intervals for them. This information allows the practitioner to decide whether provided time estimates (coupled with accuracy parameters) meet his criteria. The proposed approach can be used fo time estimations in the projects containing several operations of different nature. The application of the proposed methodology is discussed in detail for the case of fenestration industry.

Optimization of failure-prone manufacturing systems with uncertainty in demand and inventory levels are considered. Conventional approach to production optimization of manufacturing systems requires precise knowledge of demand and inventory. In case of unknown demand and imprecise inventory the online estimation is needed in order to implement optimal policies. We propose in this work a novel methodology for monitoring and online assessment of demand and inventory levels based on the state estimators in the case of precisely known inventory and on Kalman filtering in the case of uncertainty in inventory information. The proposed approach allows to continuously monitor the uncertain states of the system and provides converging estimates of demand and inventory levels (when they are not precisely measured). The cases of constant, slow-varying and randomly-varying demand are considered. Obtained estimates are shown not to be affected by the discontinuous changes in production capacity, that are due to random failure-repair processes. The proposed methodology is described in detail for the case one-machine-one-product system and the possible extensions to the case of hybrid manufacturing-remanufacturing systems with uncertain demand and return are outlined.

A failure-prone manufacturing system that consists of one machine producing one type of product is studied. The random phenomena examined are machine breakdowns and repairs. We assume that the machine undergoes a progressive deterioration while in operation and that the machine failure rate is a function of its age. The aging of the machine (the dynamics of the machine age) is assumed to be an increasing function of its production rate. Corrective maintenance activities are imperfect and restore the age of the machine to as-bad-as-old conditions. When a failure occurs, the machine can be repaired, and during production, the machine can be replaced, depending on its age. When the replacement action is selected, the machine is replaced by a new and identical one. The decision variables are the production rate and the replacement policy. The objective of this article is to address the simultaneous production and replacement policy optimization problem in the context of manufacturing with deterioration and imperfect repairs satisfying the customer demand and minimizing the total cost, which includes costs associated with inventory, backlog, production, repair and replacement, over an infinite planning horizon. We thoroughly explore the impact of the machine aging on the production and replacement policies. Particular attention is paid to the verification of underlying mathematical results that guarantee the existence of optimal solutions and the convergence of numerical methods. Due to imperfect repairs, the dynamics of the system is affected by the system history, and semi-Markov processes have to be used for modeling. Optimality conditions in the form of the Hamilton–Jacobi–Bellman equations are developed, and numerical methods are used to obtain the optimal control policies (production (rate) and replacement policies). A numerical example is given to illustrate the proposed approach, and an extensive sensitivity analysis is presented to confirm the structure of the obtained control policies.

Hybrid systems that use in their production process both raw materials (manufacturing mode), and returned products (remanufacturing mode) are considered. The system is supposed to be fully flexible and able to share its production time between manufacturing and remanufacturing. The system performance is evaluated using a piecewise linear function of serviceable and return inventories. Limited flow rate of returned products results in the state constraint on the return inventory and imposes additional limitations on the system feasibility. Such systems, to the best of the authors knowledge, were not previously considered in the literature. After characterizing manufacturing-remanufacturing strategies analytically, we propose some heuristics that approximate optimal policies in case of systems without failures, and then extend them to the case of failure-prone systems. We present the numerical study based on the solution of Hamilton-Jacobi-Bellman equations, that complements analytical results and allows to validate the proposed sub-optimal policies.

Hybrid systems that use both raw materials (manufacturing mode) and returned products (remanufacturing mode) in their production process are considered. The system consists of one facility and necessitates setup for switching from one production mode to another. Since the flow rate of returned products is limited (fixed percentage of the demand rate is considered), switching from one mode to another is unavoidable, and so production and setup scheduling becomes critical for meeting customer demand and manufacturing cost optimization. Evaluating system performance we take into account production costs (different in manufacturing and remanufacturing modes), serviceable and return inventory costs, backlog and setup costs. Analytical solutions for optimal production and setup strategies are obtained, feasibility conditions are derived, and the sensitivity of obtained results over system parameters is investigated.

This paper deals with the simultaneous production planning and quality control problem in manufacturing systems with unreliable single machine responding to a single product type demand. The machine is subject to random failures and repairs, and deteriorates with its age while in operation. This deterioration manifests by imperfect repairs and is characterized to increase the failures rates and decrease the quality of the parts produced. Because the availability and the quality of the parts of the machine decrease with repair activities, the introduction of the option to replace the machine will be taken to completely restore the age of the machine. When the replacement action is selected, the machine is replaced by a new identical one. The objective of this research is to find the simultaneous production and replacement policy under quality and failures deteriorations. The optimal solution is established in order to minimize the discounted total cost including the inventory holding, backlog, production, repair and replacement costs over an infinite planning horizon and satisfy the customer demand. Due to imperfect repairs, the semi-Markov processes are more appropriate to describe the systems subject to deteriorations caused by the machine aging. Optimality conditions are developed using the optimal control theory based on stochastic dynamic programming. Numerical methods are used to obtain the optimal control policies (production rate and replacement policies). Finally, an illustrative example and a sensitivity analysis are provided to confirm the structure of the obtained optimal control policies.

This paper deals with the production-dependent failure rates for a hybrid manufacturing/remanufacturing system subject to random failures and repairs. The failure rate of the manufacturing machine depends on its production rate, while the failure rate of the remanufacturing machine is constant. In the proposed model, the manufacturing machine is characterized by a higher production rate. The machines produce one type of final product and unmet demand is backlogged. At the expected end of their usage, products are collected from the market and kept in recoverable inventory for future remanufacturing, or disposed of. The objective of the system is to find the production rates of the manufacturing and the remanufacturing machines that would minimize a discounted overall cost consisting of serviceable inventory cost, backlog cost and holding cost for returns. A computational algorithm, based on numerical methods, is used for solving the optimality conditions obtained from the application of the stochastic dynamic programming approach. Finally, a numerical example and sensitivity analyses are presented to illustrate the usefulness of the proposed approach. Our results clearly show that the optimal control policy of the system is obtained when the failure rates of the machine depend on its production rate.

This paper presents the problem of navigation, gate recognition, and gate crossing for a real size outdoor mobile robot. The vehicle localization and general navigation is based on Global Positioning System (GPS) and Inertial Navigation System (INS). These sensors are aided by a Laser Measuring System (LMS). The laser scanner sensor gives information about the gate exact location, its shape, and vehicle attitude with respect to the gate. This necessitates the transition from GPS/INS based guidance in the open field to the range based, guidance system in proximity of the gate. A recognition procedure based on the concept of the gate signature has been developed and shown. It is followed by novel map-matching and localization procedures respectively. The developed navigation controller makes use of the polar coordinate representation and discontinuous feedback adapted for real time applications.

For a robot to be autonomous, it needs to build a representation of its environment and to locate itself. When exploring new environments, localization and map-building processes are actually coupled. Closing the loops is a challenging aspect for existing map-building methods — they are often time consuming and hardly usable for real-time applications. This paper presents a method that allows multi-loop closing by separating map building process into local and global mapping. Our method is based on the segmentation of the whole environment into “corridors” and “intersections”. The latter are used as natural landmarks: they are recognized when the robot passes second time through an already visited area. Local maps of each corridor and intersection are integrated into the global map which is updated after loop closing event. As proposed recalculations of the whole map are relatively simple, the process can be effectively used for real time applications.

Stabilization of linear systems by state feedback is an important problem of the controller design. The design of observers with appropriate error dynamics is a dual problem. This duality leads, at first glance, to the equivalence of the responses in the synthesized systems. This is true for the time-invariant case, but may not hold for time-varying systems. We limit ourselves in this work by the situation when the system itself is time invariant, and only the gains are time varying. The possibility of assigning a rapidly decaying response without peaking is analyzed. The solution of this problem for observers using time-varying gains is presented. Then we show that this result cannot be obtained for state feedback controllers. We also analyze the conditions under which the observer error dynamics and the response of the closed loop time-varying controllers are equivalent. Finally we compare our results to recently proposed observer converging in finite time and Riccati-based continuous observer with limited overshoots.

This paper describes an approach to the coordination of two car-like robots that must cooperate in accomplishing a transportation task, namely carrying a long beam that neither one can carry alone. The robots are not allowed any form of explicit exchange of information, and can therefore only "communicate" through the task that they perform together. We propose for this problem a decentralized controller that relies on a two-stage strategy. At the higher level, each robot computes, based on the information available to it, a desirable motion for the beam. The lower-level controller must then generate controls to be fed to the robot's actuators (its steering and propulsion motors), so that the beam's actual motion approximates as well as possible the desired one. This article presents our mathematical formalism and the derivation of the corresponding control laws. We present the results of simulation runs of this decentralized, two-level control strategy, as well as the experimental testbed built for studying such coordination tasks.

Autonomous navigation in an outdoor environment can be effectively performed by small robots but remains a challenging task as soon as real scale ground vehicles are concerned. An intelligent mobile robot which uses a real armor ground vehicle as a platform is currently being developed for security applications (Fig. 30.1(a)). The robot tasks needed to be addressed are patrolling, surveillance, and tracking suspicious objects in a limited area. Executing those tasks a security robot often faces the situation when many objects in the environment have similar geometrical characteristics. This situation is typical for navigating within the outdoor warehouse [1] as illustrated in Fig. 30.1(b). The cargo containers (the squares with pattern) of the same size are piled inside the fenced area. A robot is used to carry out the patrol along a given trajectory (dotted line) around the area. Being equipped with the basic positioning system using GPS receiver and odometry sensor, a robot is able to follow the given path if measurement no errors are negligible. In practice, due to various errors (misalignments, drifts, slippage) basic GPS/odometry-based system fails to provide reliable pose estimates required in physically restricted environments. Measurements of relative distances are necessary and they are provided in our case by an additionally installed laser range sensor (LRS) known for its accuracy and reliability.

Guiding an autonomous ground vehicle through the gate based on the range data from the laser scanner is considered. This kind of operation is important for security mobile robots. Information about the gate shape is supposed to be more accurate than the geographical location of the gate. This necessitates the transition from GPS-based guidance in the open field to range-based guidance in the proximity of the gate. Recognition procedure based on the proposed concept of the gate signature is followed by Map-matching and Localization. Navigation controller makes use of the polar coordinate representation and discontinuous feedback adapted for real time applications.

Obstacles detection is essential to safe autonomous platform navigation. The obstacle detection methods proposed in the literature do not pay sufficient attention to the occlusion-problem caused by the existence of regions along the trajectory of a vehicle that are hidden by other objects and where potential obstacles might be located. Our approach takes occlusions into account to prevent the possibility of collision. Experimental results with a robotic platform demonstrating the effectiveness of the developed algorithm are presented.

This paper describes an autonomous system for exploration and navigation within networks of tunnels, as those typically found in underground mines and caves. In the exploration mode, a remotely located supervisor instructs the system to move through successive sections of the network, gathering range data that is, then, concatenated into 2D/3D survey maps of the environment. In the navigation mode, the supervisor specifies high-level missions on the previously acquired survey maps. A motion planner, then, translates each mission into a set of consecutive navigation actions, separated by natural landmarks. Mission execution consists of detecting landmarks, self-localizing and performing the planned navigation actions.

The paper concerns the problem of path tracking control in the class of vehicles made up of two units with an articulation between the two. Each unit has two fixed (nonsteerable) wheels. Steering action is, thus, performed by changing the angle between the front and rear units. Such a vehicle is used for transfer of ore inside the relatively narrow and restricted underground mine galleries. The articulation in the middle helps also for better capability in curve negotiation. In operation, this vehicle usually moves with a low speed because of the environment. As a result, a number of issues, such as dynamic stability and aerodynamic forces which are important to road vehicles, do not come into effect. Furthermore, as far as the path tracking automation is concerned, the dynamics of the vehicle and tire deformation have little effect and can be neglected. Analysis and formulation of the path tracking problem, thus, can be based on the kinematics only. In this paper the control problem is formulated and verified. The synthesis of a feedback system to govern the steering action, then, becomes possible.

The paper presents the theoretical analysis and experimental results of path tracking control of a class of vehicles widely used in underground mining operations. A vehicle consists of the front and rear units hinged together, where each unit has only one pair of nonsteerable wheels. Steering is performed by changing the angle between the front and rear units by means of a (pair of) hydraulic cylinders (linear actuators). In operation this vehicle moves in either forward or backward directions. Path tracking control problem is of the main importance in order to follow the relatively narrow mining corridors. It consists of using the sensory information to measure the deviations in position and orientation from the path to be followed. Based upon these two tracking errors a feedback system must govern the appropriate steering action.

The dynamics of motion of a class of vehicles consisting of two one-axle wheeled units pivoted together are developed for the formulation of the path tracking control problem. This particular type of vehicle is frequently used for ore transportation in underground mines. Steering of this vehicle is performed through changing the angle between the two units by means of an actuator. In this paper the equations governing the motion and the tracking error dynamics in terms of the system inputs, namely the traction forces on the front and rear wheels and the actuator force for changing the angle between the two units, are derived. These equations are nonlinear and highly coupled. However, it may be deduced that from what normally appears in practice and for low operational speeds some acceptable assumptions may be made based upon which the formulation of the control problem and the synthesis of a controller becomes much simpler.

An enhanced odometry technique based on the heading sensor called "clino-gyro" that fuses the data from a fiber optic gyro and a simple inclinometer is proposed. In the proposed scheme, inclinometer data are used to compensate for the gyro drift due to roll/pitch perturbation of the vehicle while moving on the rough terrain. Providing independent information about the rotation (yaw) of the vehicle, clino-gyro is used to correct differential odometry adversely affected by the wheel slippage. Position estimation using this technique can be improved significantly, however for the long term applications it still suffers from the drifts of the gyro and translational components of wheel skidding. Fusing this enhanced odometry with the data from environmental sensors (sonars, laser range finder) through Kalman filter-type procedure a reliable positioning can be obtained. This technique has been implemented on-board of an experimental skid-steered vehicle. Obtained precision is sufficient for navigation in underground mining drifts. For open-pit mining applications further improvements can be obtained by fusing proposed localization algorithm with GPS data.

For time-varying linear systems with piecewise continuous coefficients the property of the system matrix to commute with the matriciant is shown not to require commuting with the integral. Commuting with the integral yields the possibility of matriciant representation as the exponential of the integral (Brockett) and therefore commuting with the matriciant. We show that the converse result does not hold in the class of piecewise continuous matrices. The relationship with the peaking in the systems stabilized by state feedback and by output injection is discussed.

Some properties of the transition processes in a SISO system incorporating an observer are discussed. The symmetry of the transition matrix with respect to the eigenvalues assigned for controller and observer is proved using state space methods. The interrelation with the peaking phenomenon is discussed and asymptotic behavior of the system for the case of fast observer dynamics is analyzed. Some illustrative examples are presented.