Mixed-integer programming for optimal path planning of robotic manipulators

Real-time motion planning and control of multi-joint robot manipulators are studied using neural networks. The proposed neural network approach consists of two modules: one for real-time collision-free motion planning, the other for real-time fine control of the robot manipulators. The motion planning module is a biologically inspired, parallel connected, topologically organised neural network, where each neuron is characterised by a shunting equation, whose state space is the robot configuration joint space. This module is capable of planning a real-time optimal path for robot manipulators through the dynamic activity landscape of the neural network. The motion control module involves of a feedforward neural network together with a traditional PD feedback loop. It is capable of achieving real-time fine motion control of robot manipulators under significant uncertainties and without any prior knowledge of the robot dynamics. This module can quickly compensate sudden changes in the robot dynamics. The real-time fine control of robot manipulators is achieved through the online learning of the neural network. Both the motion planning and motion control modules are computationally efficient, and their global stabilities are proved using Lyapunov stability theory.

This paper presents the construction of the artificial potential field based on discrete solution to the Laplace equation (Laplacian Artificial Potential Field, LAPF), for path planning of robotic manipulators in two-dimensional and three-dimensional representations of the configuration space (C-space). In general, the characterization of the manipulator´s workspace using the LAPF derives in obtaining a local minima space free when considering the combination of the manipulator's goal (position / orientation) as an attractive potential while obstacles are modeled as repulsive potentials.In addition it is shown the construction of three-dimensional configurations space, for a three-degree of freedom planar manipulator, with different arrangements stationary obstacles, of punctual type and bar type. In order to show the complexity of the space planning into the configuration space, as a result of the mapping of the obstacles within the manipulator's workspace not homogeneous to their representation in the joint's space.

Objectives. The work analyzes features of one of the most promising approaches to solve the problems for motion planning of autonomous robotic manipulators of various types and purposes using the rapidly exploring random tree (RRT) method. The development of modern robotics is shown to be inextricably linked with the improvement of the designs of the created samples, for which the placement of a manipulator on platform becomes a typical layout option. Prospects for using the RRT method as a constructive basis for creating a universal motion planner are evaluated for mobile and robotic manipulators, including autonomous robotic systems with a manipulator on a moving platform.Methods. The object of the research is the RRT method and its well-known modifications RRT* and RRT-Connect. The effectiveness of applying such methods for solving problems associated with planning the motions of robotic manipulators of various types was evaluated using computer and natural simulation methods.Results. Based on a review of the literature and the results of the research, the wide possibilities of the RRT method can be used for solving motion planning problems not only for mobile and robotic manipulators, but also for robotic systems on whose transport platform an onboard manipulator has been installed (including those having a redundant or reconfigurable structure). The effectiveness of the applied application of the RRT method is confirmed by examples of modeling a mobile platform with an onboard manipulator and the results of full-scale experiments with a prototype of the ARAKS reconfigurable mechatronic-modular robotic manipulators (RTU MIREA, Russia). It can be experimentally demonstrated and theoretically substantiated that the final dimension of the exploring tree, and hence the time of its construction up to reaching a given target state, is largely determined by the value of the growth factor.Conclusions. The generalization of the results obtained opens up real prospects for using the RRT method as a constructive basis not only for creating universal means for motion planning mobile robotic systems with an onboard manipulator, but also for solving the problems of automating the docking of autonomous mobile platforms.

To solve joint optimization scheduling problem of thermal power plants based on the electricity market, the constraints and characteristics of optimal operation of thermal power plants are analyzed. From the perspective of economics and environmental science, we propose and establish an electricity market based joint optimization scheduling model of thermal power plants. Mutation particle swarm optimization algorithm (MPSO) is proposed to solve the model. Using an authentication instance, we compare and analyze the performances of the MPSO method and the mixed integer programming (MIP) method in solving the model. Further, considering a commonly used system, we show the efficiency of the MPSO method in solving the model; we apply two case studies to illustrate the performance of the MPSO method in solving the thermal unit commitment (UC) problem. To demonstrate the effectiveness of the MPSO method in solving the UC problem, we use MPSO method, PSO-LR (Lagrangian relaxation) [H. H. Balci and J. Valenzuela, Int. J. Appl. Math. Comput. Sci. 14(3), 411–421 (1989)], improved PSO [B. Zhao et al., Elect. Power Energy Syst. 28, 482–490 (2006)], mimetic algorithm [J. Valenzuela and A. Smith, J. Heuristics 8(2), 173–195 (2002)], adaptive LR [W. Ongsakul and N. Petcharaks, IEEE Trans. Power Syst. 19(1), 620–628 (2004)], stochastic priority list (PL) [T. Senjyu et al., Electr. Power Syst. Res. 76, 283–292 (2006)], PL based evolutionary algorithm [D. Srinivasan and J. Chazelas, in International Conference on Power System Technology (2004), Vol. 90, pp. 1746–1751], enhanced adaptive LR [W. Ongsakul and N. Petcharaks, IEEE Trans. Power Syst. 19(1), 620–628 (2004)], mixed-integer linear programming (MILP) [M. Carrin and J. M. Arroyo, IEEE Trans. Power Syst. 21(1), 321–332 (2006)], MILP [G. Morales-Espana et al., IEEE Trans. Power Syst. 28, 4897 (2013)], NBD [T. Niknam et al., Appl. Energy 86, 1667–1674 (2009)], generalized new benders decomposition approach (NBD) [S. Rahimi et al., World Appl. Sci. J. 6(12), 1665–1672 (2009)], LR and genetic algorithm[C. P. Cheng et al., IEEE Trans. Power Syst. 15(2), 707–714 (2000)], and seeded memetic algorithm (SMA) [J. Valenzuela and A. Smith, J. Heuristics 8(2), 173–195 (2002)] to solve the UC problem, simulation results are compared with the ones obtained by other methods. It is shown that the optimal operation model is right, the MPSO method is better than MIP method in solving the model, and they have universality. The effectiveness of the MPSO method in solving the UC problem is better than other methods. The MPSO method has better solutions in comparison with other methods, especially for systems with a large number of units.

The problem of fitting continuous piecewise linear (PWL) functions to discrete data has applications in pattern recognition and engineering, amongst many other fields. To find an optimal PWL function, the positioning of the breakpoints connecting adjacent linear segments must not be constrained and should be allowed to be placed freely. Although the univariate PWL fitting problem has often been approached from a global optimisation perspective, recently, two mixed-integer linear programming approaches have been presented that solve for optimal PWL functions. In this paper, we compare the two approaches: the first was presented by Rebennack and Krasko [Rebennack S, Krasko V (2020) Piecewise linear function fitting via mixed-integer linear programming. INFORMS J. Comput. 32(2):507–530] and the second by Kong and Maravelias [Kong L, Maravelias CT (2020) On the derivation of continuous piecewise linear approximating functions. INFORMS J. Comput. 32(3):531–546]. Both formulations are similar in that they use binary variables and logical implications modelled by big-[Formula: see text] constructs to ensure the continuity of the PWL function, yet the former model uses fewer binary variables. We present experimental results comparing the time taken to find optimal PWL functions with differing numbers of breakpoints across 10 data sets for three different objective functions. Although neither of the two formulations is superior on all data sets, the presented computational results suggest that the formulation presented by Rebennack and Krasko is faster. This might be explained by the fact that it contains fewer complicating binary variables and sparser constraints. Summary of Contribution: This paper presents a comparison of the mixed-integer linear programming models presented in two recent studies published in the INFORMS Journal on Computing. Because of the similarity of the formulations of the two models, it is not clear which one is preferable. We present a detailed comparison of the two formulations, including a series of comparative experimental results across 10 data sets that appeared across both papers. We hope that our results will allow readers to take an objective view as to which implementation they should use.

In this paper, we formulate the problem of finding an optimal generation dispatch and transmission topology to meet a specific inflexible load as a mixed integer program. Our model is a mixed-integer linear program because it employs binary variables to represent the state of the equipment and linear relationships to describe the physical system. We find that on the standard 118-bus IEEE test case a savings of 25% in system dispatch cost can be achieved.

In recent years, a number of trajectory optimization algorithms have been proposed and established for motion planning of robot manipulators in complex, but static, predefined environments. To enable reactive motion planning under uncertain conditions caused, for example, by moving obstacles, this paper proposes a formulation of the trajectory optimization problem that is tailored for model predictive control. The proposed algorithmic solution leverages off-the-shelf computational tools for nonlinear model predictive control, optimization, and collision checking. In addition, a motion planning paradigm is introduced to allow for online collision-free motion when following a joystick command. The approach is validated in the context of an industrial pick-and-place application using MATLAB® and a Kinova® robot manipulator, both in simulation and with actual hardware.

Purpose – This paper aims to address the problem of optimal allocation of demand of items among candidate suppliers to maximize the purchase value of items. The purchase value of the items directly relates to cost and quality of raw materials purchased from the supplier. In an increasingly competitive environment, firms are paying more attention to selecting the right suppliers for procurement of raw materials and component parts for their products. The present research work focuses on this issue of supply chain management. Design/methodology/approach – This present research work devises a hybrid algorithm for multi-period demand allocation among the suppliers. The customer demand is allocated by using a hybrid algorithm based on the technique for order preference by similarity to ideal solution (TOPSIS), fuzzy set theory and the mixed linear integer programming (MILP) approaches. Findings – The supply chain network is witnessing a changing business environment due to government policies aimed at promoting new small manufacturing enterprises (small and medium-sized enterprises) for intermediate parts and components. Hence, the managers have an option to select a new group of suppliers and allocate the optimal multi-period demand among the new group of suppliers to maximize their purchase value. In this context, the proposed hybrid model would be beneficial for the managers to operate their supply chain effectively and efficiently. The present research work will be helpful for the managers who are interested to reconfigure their supply chain under the failure of any supply chain partner or in a changing business environment. The model provides flexibility to the managers for evaluation of the different available alternatives to take a decision of optimal demand allocation among the suppliers. The proposed hybrid (fuzzy, TOPSIS and MILP) model provides more objective information for supplier evaluation and demand allocation among suppliers in a supply chain. The managers can use the proposed model to the analysis of other management decision-making problems. Originality/value – This present research work devises a hybrid algorithm for multi-period demand allocation among the suppliers. This hybrid algorithm prioritizes the suppliers and then allocates the multi-period demand among the suppliers. The customer demand is allocated by using a hybrid algorithm based on the technique for order preference by similarity to ideal solution (TOPSIS), fuzzy set theory and the mixed linear integer programming (MILP) approaches.

The redundancy allocation problem (RAP) aims to find an allocation of redundant components that maximizes system reliability under resource constraints. In this paper, we consider the RAP for complex systems with heterogeneous components, which may have bridges or interconnecting subsystems and are generally more complicated in structure than commonly studied series-parallel systems. A major challenge of the RAP is that the reliability function is nonlinear. To tackle this, we develop six exact mixed integer linear programming (MILP) formulations, which, to our knowledge, are the first of such formulations for the problem. The key idea is to use binary variables and big-M constraints to successively linearize each product term in the reliability function. In addition, we propose a novel tree representation of the reliability function to establish the interconnections between different product terms, which is then used to reduce the number of decision variables and constraints needed in the linearization. We also propose an alternative form of the reliability function that only involves the failure probabilities of subsystems, and leverage this to derive better variable bounds, smaller big-M constants, and simpler formulations. We compare the six MILP formulations by solving them directly using an MILP solver based on three sets of test instances of varying complexity. Results indicate that all formulations achieve optimal solutions quickly for the first set and within reasonable computation times for the second set. For the third set, two formulations can always be solved within a given time limit. Overall, the MILP formulation derived based on the alternative form of the reliability function and a specific type of tree representation scheme performs the best. We also demonstrate that our approach is more robust and scalable than a benchmark branch-and-bound method. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by National Natural Science Foundation of China [Grants 72310107003, 72471189, 71901176]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0842 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0842 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Flowshop scheduling via mixed integer linear programming (MILP) has received considerable attention in the past four decades. However, alternate models are limited; most numerical studies have used small problem sizes. A need for good model evaluation methodology exists; and limited work exists on flowshops with no intermediate storage. This paper presents a classification of flowshops and MILP scheduling models, and addresses some of these issues. It develops a host of new MILP formulations for minimizing makespan in a permutation flowshop with no storage and with or without unit setups. It presents some useful insights into model building by employing a variety of new and old binary variables and coupling them creatively. In contrast to previous work, it evaluates a range of new and existing MILP models using many larger test problems with no or unlimited intermediate storage, and presents a reliable procedure to rank various models based on problems with varying data and sizes. It shows that the top models for the two flowshops indeed show slightly different computational performance.

Determining [formula omitted]- and [formula omitted]-robustness of digraphs using mixed integer linear programming

This article discusses nonprehensile manipulation of an asymmetric object using a robotic manipulator from a motion planning point of view. Four different aspects of the problem will be analyzed:object stability, motion planning, manipulator control, and experimental validation. Specifically, via an analysis of marginal stability of an object resting on a moving tray, the work establishes the critical accelerations of the manipulator's end-effector, below which the object's stability is guaranteed. These critical accelerations guide the design of the end-effector's motion for successful nonprehensile manipulation of the object. In particular, we propose two methods to formulate polynomial asymmetric s-curve trajectories such that the end-effector completes its motion in minimum time. In one method, the trajectory is divided into segments whose time intervals are then computed via a recursive algorithm. In the other method, we formulate an optimization problem and design the minimum-time trajectory by balancing the tradeoff between the travel time and actuator effort. A series of experiments with a robotic arm is designed to validate and compare these motion planning methods in the context of nonprehensile manipulation. In addition, the experimental results demonstrate the advantages of the asymmetric s-curve motion profiles over the traditional symmetric s-curves.

ABSTRACTRailway disturbance management is inherently a multi-objective optimization problem that concerns both the operators’ cost and passenger’s service level. This study proposes a multi-objective simulation-based optimization framework to effectively manage the train conflicts after the occurrences of a disturbance caused by a temporary line blockage. The simulation model enhanced with a dynamic priority dispatching rule in order to speed up the optimization procedure. A multi-objective variable neighborhood search meta-heuristic is proposed to solve the train rescheduling model. The obtained Pareto optimal solutions for disturbance management model support the decision maker to find a trade-off between both user and operator viewpoints. The proposed approach has been validated on a set of disruption scenarios covering a large part of the Iranian rail network. The computational results prove that the proposed model can generate good-quality timetables with the minimum passenger delay and deviation from the initial timetable. The outcomes indicate that the developed simulation-based optimization approach has substantial advantages in producing practical solution quickly when compared to currently accepted solutions.Abbreviation: MOVNS: multi-objective variable neighbourhood search; DES: discrete-event simulation; SO: simulation-optimization; AG: Alternative Graph; FCFS: First Come First Served; MIP: mixed integer programming; MILP: mixed-integer linear programming; B&B: branch and bound algorithm; VND: Variable Neighborhood Descent; NSGA-II: Non-dominated Sorting Genetic Algorithm–II; CD: crowding distance; DP: dynamic priority; EDD: earliest due date first; SRTT: shortest remaining traveling time; LST: least slack time first

We present an optimization-based motion planning algorithm to compute a smooth, collision-free trajectory for a manipulator used to transfer a liquid from a source to a target container. We take into account fluid dynamics constraints as part of the trajectory computation. In order to avoid the high complexity of exact fluid simulation, we introduce a simplified dynamics model based on physically inspired approximations and system identification. Our optimization approach can incorporate various other constraints such as collision avoidance with obstacles, kinematic and dynamics constraints of the manipulator, and fluid dynamics characteristics. We demonstrate the performance of our planner on different benchmarks corresponding to various obstacles and container shapes. We also evaluate its accuracy by validating the motion plan using an accurate but computationally costly Navier-Stokes fluid simulation.

This paper investigates the motion planning of redundant free-floating manipulators with seven prismatic joints. On the earth, prismatic-jointed manipulators could only position their end-effectors in a desired way. However, in space, the end-effectors of free-floating manipulators can achieve both the desired orientation and desired position due to the dynamical coupling between manipulator and satellite movement, which is formally expressed by linear and angular momentum conservation laws. In this study, a tractable algorithm particle swarm optimization combined with differential evolution (PSODE) is provided to deal with the motion planning of redundant free-floating prismatic-jointed manipulators, which could avoid the pseudo inverse of the Jacobian matrix. The polynomial functions, as argument in sine functions are used to specify the joint paths. The coefficients of the polynomials are optimized to achieve the desired end-effector orientation and position, and simultaneously minimize the unit-mass-kinetic energy using the redundancy. Relevant simulations prove that this method provides satisfactory smooth paths for redundant free-floating prismatic-jointed manipulators. This study could help to recognize the advantages of redundant prismatic-jointed space manipulators.