Globally Optimal Redundancy Resolution with Dynamic Programming for Robot Planning: A ROS Implementation

Redundancy resolution schemes based on calculus of variations present several drawbacks limiting the intrinsic potential, in terms of augmented dexterity and flexibility, of redundant manipulators. In particular, they do not guarantee the achievement of the globally-optimal solution. Grid search algorithms can be designed starting from dynamic programming (DP) which overcome the limits of calculus of variations. This paper, in particular, presents a novel algorithm that considers the employment of multiple DP grids to be searched together at the same time. Such a technique achieves the global optimum, while allowing for pose reconfiguration of the manipulator while the task is executed.

The obstacle avoidance controller is a key autonomous component which involves the control of tractor system dynamics, such as the yaw lateral dynamics, the longitudinal dynamics, and nonlinear constraints including the speed and steering angles limits during the path-tracking process. To achieve the obstacle avoidance ability of control accuracy, an independent path re-planning controller is proposed based on ROS (Robot Operating System) nonlinear model prediction in this paper. In the design process, the obstacle avoidance function and an objective function are introduced. Based on these functions, the obstacle avoidance maneuvering performance is transformed into a nonlinear quadratic optimization problem with vehicle dynamic constraints. Moreover, the tractor dynamics maneuvering performance can be effectively adjusted through the proposed objective function. To validate the proposed algorithm, a ROS based tractor dynamics model and the SLAM (Simultaneous Localization and Mapping) are established for numerical simulations under different speed. The maximum obstacle avoidance deviation in the simulation is 0.242 m at 10 m/s, and 0.416 m at 30 m/s. The front-wheel rotation angle and lateral velocity are within the constraint range during the whole tracking process. The numerical results show that the designed controller can achieve the tractor obstacle avoidance ability with good accuracy under different conditions. Keywords: ROS, obstacle avoidance, nonlinear model prediction, agricultural tractor DOI: 10.25165/j.ijabe.20191206.4907 Citation: Liu Z D, Lv Z Q, Zheng W X, Zhang W Z, Cheng X X. Design of obstacle avoidance controller for agricultural tractor based on ROS. Int J Agric & Biol Eng, 2019; 12(6): 58–65.

Many continuous process industries are required to operate multiproduct supply chains under significant uncertainty in market demands and prices, and mathematical programming formulations have been developed for the deterministic version of the problem. However, available extensions to the stochastic case cannot be readily used to obtain an optimal operating policy in practice because the uncertainty results in an explosion of the scenarios to be considered over an extended time horizon. In this article we represent the uncertainty through Markov chains and use an approach based on stochastic dynamic programming (DP), which can generate a dynamic operating policy that incorporates information about the uncertainty in the problem at each time step. DP is computationally infeasible because of the size of the state and action space for realistic problems. We propose a novel stochastic optimization algorithmic framework called “DP in a heuristically restricted state space.” The confined state space is generated by simulating various potential scenarios under centralized dynamic inventory and production policy generated by combining static local inventory policy heuristics. The resulting DP policy responds to the time‐varying demand for products by appropriately stitching together decisions made by the local static policies. This is a new formulation for effectively combining heuristic policies. © 2006 American Institute of Chemical Engineers AIChE J, 2006

In this paper, we present a sampling-based verification algorithm for embedded robotic systems with continuous dynamics and uncertainty due to adversaries, unmodeled disturbance inputs, unknown parameters, or initial conditions. The algorithm attempts to find inputs (and resulting trajectories) that falsify the specifications of the system thus providing examples of bad inputs to the system. The system is said to be verified if the algorithm cannot find falsifying inputs. The main contribution of the paper is the analysis of the effects of discretization of the state and input spaces that are inherent to sampling-based techniques. We derive conditions that guarantee resolution completeness. These provide sufficient, although conservative, conditions for verifying Lipschitz continuous (but possibly non-smooth) dynamic systems without known analytical solutions. We analyze the effects of transformations of the input and state space on these conditions. The main results of this paper are illustrated with several simple examples.

This paper treats a class of finite-stage dynamic programming (DP) problems whose state space is an interval in the one-dimensional Euclidean space R1. By introducing a notion of “reward space” we can define, in this class, an inverse problem (called the inverse DP) to a given DP (called the main DP), because of the monotonicity and continuity of the reward functions and state transformations. Roughly speaking the inverse DP to the main DP is defined by replacing “max”, “reward functions” and “state transformations” with “min”, “inverse (in some sense) to the state transformations” and “inverse (in some sense) to the reward functions”, respectively, by replacing “terminal reward function” with “inverse to itself”, and by alternating “reward spaces” with “state spaces”, but by letting “action spaces” remain as they are. According to the monotonicity of the reward functions and state transformations we clarify the relation between the main DP and the inverse DP separately for four cases. Our main result is stated as follows. The pair of optimal reward functions and optimal policy for the main DP characterizes, in an inverse sense, the pair of optimal reward functions and optimal policy for the inverse DP, and vice versa (Section 2). Further we show that our DP represents a mathematical programming problem which has the property “recursiveness with monotonicity” in [5] and conversely such a problem can also be represented by our DP (Section 3). The last section is devoted to the illustration of several examples.

Dynamic Programming (DP) technique is an effective algorithm to find the global optimum. However when applying DP for finite state problems, if the state variables are discretized, it increases the cumulative errors and leads to suboptimal results. In this paper we develop and present a new DP algorithm that overcomes the above problem by eliminating the need to discretize the state space by the use of sets. We show that the proposed DP leads to a globally optimal solution for a discrete time system by minimizing a cost function at each time step. To show the efficacy of the proposed DP, we apply it to optimize the fuel economy of the series and parallel Hybrid Electric Vehicle (HEV) architectures and the case study of Chevrolet Volt 2012 and the Honda Civic 2012 for the series and parallel HEV’s respectively are considered. Simulations are performed over predefined drive cycles and the results of the proposed DP are compared to previous DP algorithm (DPdis). The proposed DP showed an average improvement of 2.45% and 21.29% over the DPdis algorithm for the series and the parallel HEV case respectively over the drive cycles considered. We also propose a real time control strategy (RTCS) for online implementation based on the concept of Preview Control. The RTCS proposed is applied for the series and parallel HEV’s over the drive cycles and the results obtained are discussed.

In this paper we propose an algorithm for the constrained two-dimensional cutting stock problem (TDC) in which a single stock sheet has to be cut into a set of small pieces, while maximizing the value of the pieces cut. The TDC problem is NP-hard in the strong sense and finds many practical applications in the cutting and packing area. The proposed algorithm is a hybrid approach in which a depth-first search using hill-climbing strategies and dynamic programming techniques are combined. The algorithm starts with an initial (feasible) lower bound computed by solving a series of single bounded knapsack problems. In order to enhance the first-level lower bound, we introduce an incremental procedure which is used within a top-down branch-and-bound procedure. We also propose some hill-climbing strategies in order to produce a good trade-off between the computational time and the solution quality. Extensive computational testing on problem instances from the literature shows the effectiveness of the proposed approach. The obtained results are compared to the results published by Alvarez-Valdes et al. (2002).

The redundancy resolution schemes based on the optimization of an integral performance index are investigated from the topological point of view. The topological notions of self-motion manifold, C-path-homotopy and extended aspect are clarified in relation to the limitations of the necessary conditions of optimality provided by calculus of variations. On one hand, they do not guarantee the achievement of the optimal solution, and on the other hand, they translate into a two-point boundary value problem (TPBVP), whose resolution, under certain circumstances, may not lead to a feasible solution at all. In response to the limitations of calculus of variations, a dynamic-programming-inspired formalism is developed, which is based on the discretization of the state space and on its representation in the form of multiple grids. Building upon the topological analysis, effective algorithms are designed that are able to find the optimal solution in any condition, across all C-path homotopy classes and self-motion manifolds, with no limitation due to the passage through singularities. Moreover, if the grids are representative of the manipulator’s extended aspects, the topological notion of the transitional point can be used to reduce the computational complexity of the optimal redundancy resolution algorithm. The results are demonstrated on a canonical 4R planar robot in two different scenarios.

Determination of control and state space trajectory which realizes given output time history of nonlinear dynamic system is considered in the paper. Necessary and sufficient conditions for existence of solution are formulated for a class of systems described by ordinary differential equations X=F(t,X,U) with right hand side as a vector function of class Cn, where n is dimension of state space. Existence and uniqueness of solution are studied as a local system properties, i.e in the viciniti of considered point in state and input space. A procedure which leads to a solution by means of system of nonlinear algebraic equations and classical initial-value problem solving is presented.

In this paper an optimal controller based on Action Dependent Heuristic Dynamic Programming (ADHDP) approach has been proposed for multi area Automatic Generation Control (AGC) scheme. A competitive environment has been considered in the interconnected power system. Conventional AGC model has been modified to include bilateral transactions taking place in the energy market. To implement the ADHDP approach discrete model of modified AGC scheme has been utilized. ADHDP is a powerful technique of Approximate Dynamic Programming, used for providing optimal solution by minimizing the given objective function. The proposed approach has been tested on two area AGC scheme for different cases. The results have been compared with the discrete full state feedback controller.

On-orbit Servicing, Assembly, and Manufacturing (OSAM) has emerged as a key focus for space exploration and infrastructure development, attracting interest from government agencies, the military, and private industry. The ability to inspect, repair, and maintain spacecraft while in orbit is crucial for extending mission lifetimes, reducing costs, and enabling more complex space operations. This paper presents a novel approach to the in-orbit inspection and repair of defects on spacecraft exteriors. The proposed system utilizes a 3D laser scanner mounted on an articulated robotic arm to scan the exterior of a spacecraft. The scanner generates a high-resolution point cloud of the spacecraft hull, which is compared to a previously stored baseline scan of the undamaged spacecraft. Discrepancies between the two point clouds, representing defects, are automatically detected, and localized through advanced comparison algorithms. This automated defect identification is crucial for precise, autonomous maintenance. Once a defect is identified, the data is transmitted to a central processing unit (CPU) via Robot Operating System 2 (ROS2). ROS2, while not a perfect representation of the communication protocols used in space, serves as a practical simulation for on-Earth applications, offering flexibility for multi-robot real-time communication. The CPU processes the defect data and uses a material property database along with intelligent topology optimization algorithms to design an efficient repair strategy. These algorithms compute the optimal distribution of repair material, ensuring minimal waste while restoring structural integrity. A path planning algorithm is then used to generate an optimal route for a small mobile robot, which is responsible for delivering the repair material to the defect site. For the proof-of-concept, the Dijkstra algorithm is employed to compute the shortest path while avoiding obstacles. The robot receives the computed coordinates through ROS2 and navigates to the defect location. Upon reaching the defect, the mobile robot uses an onboard localization system and fuzzy logic controller (FLC) to navigate the spacecraft surface accurately. Fuzzy logic control is particularly suitable for this application as it allows the robot to handle imprecise input, such as slight errors in localization or unexpected obstacles, ensuring smooth and adaptive navigation. Once positioned, the robot applies the required repair material, completing the task autonomously. This work demonstrates a comprehensive and scalable framework for autonomous in-orbit servicing, integrating 3D scanning, defect detection, path planning, and repair operations. The results show the potential for this system to address a wide range of spacecraft maintenance challenges. Future work will analyze different mobile robot architectures, use more adaptive localization and path-planning algorithms, and extend the platform’s capabilities to more complex repair scenarios.

The use of computer vision in the industry has become fundamental, playing an essential role in areas such as quality control and inspection, object recognition/tracking, and automation. Despite this constant growth, robotic cell systems employing computer vision encounter significant challenges, such as a lack of flexibility to adapt to different tasks or types of objects, necessitating extensive adjustments each time a change is required. This highlights the importance of developing a system that can be easily reused and reconfigured to address these challenges. This paper introduces a versatile and adaptable framework that exploits Computer Vision and the Robot Operating System (ROS) to facilitate pick-and-place operations within robotic cells, offering a comprehensive solution for handling and sorting random-flow objects on conveyor belts. Designed to be easily configured and reconfigured, it accommodates ROS-compatible robotic arms and 3D vision systems, ensuring adaptability to different technological requirements and reducing deployment costs. Experimental results demonstrate the framework’s high precision and accuracy in manipulating and sorting tested objects. Thus, this framework enhances the efficiency and flexibility of industrial robotic systems, making object manipulation more adaptable for unpredictable manufacturing environments.

An examination is made of the dynamic programming technique implemented on a distributed-memory multiprocessor system. The matrix chain product algorithm is investigated as an example problem. A method for parallelizing the dynamic programming technique for solving the matrix chain product problem is presented and load-balancing considerations are examined. The sequential dynamic programming technique is a fine grain algorithm and considered by many researchers to be too fine grain to execute effectively on a hypercube. The parallel algorithm yielded modest speedups for fixed-size problems. Scaled problems promise even better speedups. Results show that respectable performance for the dynamic programming algorithmic technique can be achieved on a hypercube. >

Computer analysis and simulation based design optimization requires more computationally efficient global optimization tools. In this work, a new global optimization algorithm based on design experiments, region elimination and response surface model, namely Approximated Unimodal Region Elimination Method (AUREM), is introduced. The approach divides the field of interest into several unimodal regions using design experiment data; identify and rank the regions that most likely contain the global minimum; form a response surface model with additional design experiment data over the most promising region; identify its minimum, remove this processed region, and move to the next most promising region. By avoiding redundant searches, the approach identifies the global optimum with reduced number of objective function evaluations and computation effort. The new algorithm was tested using a variety of benchmark global optimization problems and compared with several widely used global optimization algorithms. The experiments results present comparable search accuracy and superior computation efficiency, making the new algorithm an ideal tool for computer analysis and simulation black-box based global design optimization.

A numerical method for hybrid optimal control based on dynamic programming