Problem Of Motion Planning Research Articles

Multi-robot motion planning for unit discs with revolving areas

We study the problem of motion planning for a collection of n labeled unit disc robots in a polygonal environment. We assume that the robots have revolving areas around their start and final positions: that each start and each final is contained in a radius 2 disc lying in the free space, not necessarily concentric with the start or final position, which is free from other start or final positions. This assumption allows a weakly-monotone motion plan, in which robots move according to an ordering as follows: during the turn of a robot R in the ordering, it moves fully from its start to final position, while other robots do not leave their revolving areas. As R passes through a revolving area, a robot R′ that is inside this area may move within the revolving area to avoid a collision. Notwithstanding the existence of a motion plan, we show that minimizing the total traveled distance in this setting, specifically even when the motion plan is restricted to be weakly-monotone, is APX-hard, ruling out any polynomial-time (1+ε)-approximation algorithm.On the positive side, we present the first constant-factor approximation algorithm for computing a feasible weakly-monotone motion plan. The total distance traveled by the robots is within an O(1) factor of that of the optimal motion plan, which need not be weakly monotone. Our algorithm extends to an online setting in which the polygonal environment is fixed but the initial and final positions of robots are specified in an online manner. Finally, we observe that the overhead in the overall cost that we add while editing the paths to avoid robot-robot collision can vary significantly depending on the ordering we chose. Finding the best ordering in this respect is known to be NP-hard, and we provide a polynomial time O(log⁡nlog⁡log⁡n)-approximation algorithm for this problem.

Navigation of a compartmentalized robot system

After making progression in developing the fundamental problems related to single-robot control, many researchers swerved and diverged their focus to studying multi-robot coordination. This research aims to take the motion planning and control (MPC) problem of a multi-robot system into a new space by considering a compartmentalized robot. An efficient variant of globally rigid formation, in which multiple car-like units are adjoint and move in parallel without collisions. The motion is governed by one of the sub-units acting as a leader, while other units maintain the fixed distance amongst each other and the leader in a rigid formation. The minimum distance technique is an important input to facilitate collision avoidance, robot decision making, and robot navigation. In this study a novel method to analytically compute the minimum distance between the closest point on the line segments of rectangular protective region and the obstacle is presented. Utilizing the Lyapunov-based Control Scheme a set of autonomous controllers are designed. Computer simulations of the proposed Lyapunov-based controllers for the compartmentalized robot are presented in interesting scenarios to show the efficacy of the unique set of controllers. In these simulations, the compartmentalized robot shows strict maintenance of a rigid formation with efficient collision and obstacle avoidance. The results open up research in the design and implementation of controllers by considering multiple compartmentalized robots into swarm models, splitting and re-joining units, and applying rotational leadership ideas.

Dictionary-based experiment design for estimation of marine models

In this work, experiment design for marine vessels is explored. A dictionary-based approach is used, i.e., a systematic way of choosing the most informative combination of independent experiments out of a predefined set of candidates. This idea is quite general but is here tailored to an instrumental variable (IV) estimator with zero-mean instruments. This type of estimator is well-suited to deal with parameter estimation for second-order modulus models, which is a class of models often used to describe motion of marine vessels. The method is evaluated using both simulated and real data, the latter from a small model ship as well as from a full-scale vessel. Further, a standard motion-planning problem is modified to account for the prior-made choice of information-optimal sub-experiments, which makes it possible to obtain a plan for the complete experiment in the form of a feasible trajectory.

Learning to Search in Task and Motion Planning With Streams

Task and motion planning problems in robotics combine symbolic planning over discrete task variables with motion optimization over continuous state and action variables. Recent works such as PDDLStream [1]garrett2020pddlstream have focused on optimistic planning with an incrementally growing set of objects until a feasible trajectory is found. However, this set is exhaustively expanded in a breadth-first manner, regardless of the logical and geometric structure of the problem at hand, which makes long-horizon reasoning with large numbers of objects prohibitively time-consuming. To address this issue, we propose a geometrically informed symbolic planner that expands the set of objects and facts in a best-first manner, prioritized by a Graph Neural Network that is learned from prior search computations. We evaluate our approach on a diverse set of problems and demonstrate an improved ability to plan in difficult scenarios. We also apply our algorithm on a 7DOF robotic arm in block-stacking manipulation tasks.

KDF: Kinodynamic Motion Planning via Geometric Sampling-Based Algorithms and Funnel Control

We integrate sampling-based planning techniques with funnel-based feedback control to develop KDF, a new framework for solving the kinodynamic motion-planning problem via funnel control. The considered systems evolve subject to complex, nonlinear, and uncertain dynamics (also known as differential constraints). First, we use a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">geometric</i> planner to obtain a high-level safe path in a user-defined extended free space. Second, we develop a low-level funnel control algorithm that guarantees safe tracking of the path by the system. Neither the planner nor the control algorithm uses information on the underlying dynamics of the system, which makes the proposed scheme easily distributable to a large variety of different systems and scenarios. Intuitively, the funnel control module is able to implicitly accommodate the dynamics of the system, allowing hence the deployment of purely geometrical motion planners. Extensive computer simulations and hardware experiments with a 6-DOF robotic arm validate the proposed approach.

A Punishment Mechanism-Combined Recurrent Neural Network to Solve Motion-Planning Problem of Redundant Robot Manipulators.

In order to make redundant robot manipulators (RRMs) track the complex time-varying trajectory, the motion-planning problem of RRMs can be converted into a constrained time-varying quadratic programming (TVQP) problem. By using a new punishment mechanism-combined recurrent neural network (PMRNN) proposed in this article with reference to the varying-gain neural-dynamic design (VG-NDD) formula, the TVQP problem-based motion-planning scheme can be solved and the optimal angles and velocities of joints of RRMs can also be obtained in the working space. Then, the convergence performance of the PMRNN model in solving the TVQP problem is analyzed theoretically in detail. This novel method has been substantiated to have a faster calculation speed and better accuracy than the traditional method. In addition, the PMRNN model has also been successfully applied to an actual RRM to complete an end-effector trajectory tracking task.

An Optimal Smooth-Path Motion Planning Method for a Car-like Mobile Robot

This paper proposes an optimal motion planning method consisting of a genetic algorithm (GA), potential field (PF), and Dubins curve for a Car-like mobile robot to solve the problem of finding the shortest and most feasible path in the global environment. Firstly, the GA finds the shortest path by evaluating, selecting, crossing over, and mutating from the initial population and finally provides the strongest individual evolution. Then the result from the GA is further applied with the PF algorithm to improve the ability of obstacle avoidance in the environment. Finally, the Dubins curve method is combined to smooth the path and helps the Car-like mobile robot solve the nonholonomic constraints problem. The major advantages of this method include finding the shortest path, improving avoidance obstacle ability, and smoothing the output path in an environment effectively. The simulation of the proposed method is executed on MATLAB to verify the ability to solve motion planning problems for a Car-like mobile robot.

Many Faces of Singularities in Robotics

In this survey paper some issues concerning a singularity concept in robotics are addressed. Singularities are analyzed in the scope of inverse kinematics for serial manipulator, a motion planning task of nonholonomic systems and the optimal control covering a large area of practical robotic systems. An attempt has been made to define the term singularity, which is independent on a specific task. A few classifications of singularities with respect to different criteria are proposed and illustrated on simple examples. Singularities are analyzed from a numerical and physical point of view. Generally, singularities pose some problems in motion planning and/or control of robots. However, as illustrated on the example on force/momenta transformation in serial manipulators, they can also be desirable is some cases. Singularity detection techniques and some methods to cope with them are also provided. The paper is intended to be didactic and to help robotic researchers to get a general view on the singularity issue.

Search-based task and motion planning for hybrid systems: Agile autonomous vehicles

To achieve optimal robot behavior in dynamic scenarios we need to consider complex dynamics in a predictive manner. In the vehicle dynamics community, it is well know that to achieve time-optimal driving on low friction surface, the vehicle should utilize drifting. Hence, many authors have devised rules to split circuits and employ drifting on some segments. These rules are suboptimal and do not generalize to arbitrary circuit shapes (e.g., S-like curves). So, the question “When to go into which mode and how to drive in it?” remains unanswered. To choose the suitable mode (discrete decision), the algorithm needs information about the feasibility of different modes (continuous motion). This makes it a class of Task and Motion Planning (TAMP) problems, which are known to be hard to solve optimally in real-time. In the AI planning community, search methods are commonly used. However, they cannot be directly applied to TAMP problems due to the continuous component. Here, we present a search-based method that effectively solves this problem and efficiently searches in a highly dimensional state space with nonlinear and unstable dynamics. The space of the possible trajectories is explored by sampling different combinations of motion primitives guided by the search. Our approach allows to use multiple locally approximated models to generate motion primitives (e.g., learned models of drifting) and effectively simplify the problem without losing accuracy. The algorithm performance is evaluated in simulated driving on a mixed-track with segments of different curvatures (right and left). Our code is available at https://git.io/JenvB.

Long-Horizon Multi-Robot Rearrangement Planning for Construction Assembly

Robotic assembly planning enables architects to explicitly account for the assembly process during the design phase, and enables efficient building methods that profit from the robots' different capabilities. Previous work has addressed planning of robot assembly sequences and identifying the feasibility of architectural designs. This paper extends previous work by enabling planning with large, heterogeneous teams of robots. We present a planning system which enables parallelization of complex task and motion planning problems by iteratively solving smaller subproblems. Combining optimization methods to solve for manipulation constraints with a sampling-based bi-directional space-time path planner enables us to plan cooperative multi-robot manipulation with unknown arrival-times. Thus, our solver allows for completing subproblems and tasks with differing timescales and synchronizes them effectively. We demonstrate the approach on multiple case-studies to show the robustness over long planning horizons and scalability to many objects and agents of our algorithm. Finally, we also demonstrate the execution of the computed plans on two robot arms to showcase the feasibility in the real world.

Motion planning problem for a class of hyperbolic PDEs

The purpose of this paper is to investigate the motion planning problem (MPP) for a class of hyperbolic PDEs with a boundary control. Precisely, we aim to construct an input control leading the state output to track a given (sufficiently smooth) target trajectory. First, we establish a solution of the MPP in the form of a boundary state-feedback law. Second, we provide an explicit expression of the whole state of the resulting closed-loop. Third, we furnish an explicit formula of the MP control via the target trajectory and the solution of an appropriate PDE. Besides, the provided control leads to a complete matching of the output with the predefined trajectory at any instant. The control problem is reformulated in the context of operator semigroup theory and solved using the Laplace transform of a suitable input-output function.

Global Controllability Criteria and Motion Planning of Regular Affine Systems With Drifts

In this article, we give a condition for the global controllability of affine nonlinear control systems with drifts on Euclidean spaces. Under regularity assumptions, the condition is necessary and sufficient in the codimension-1 and codimension-2 cases, and holds for systems of higher codimensions under mild restrictions. We then investigate motion planning problems for codimension-1 affine systems, and give proof of the global existence of the lift to control curves for certain drifted systems using the homotopy continuation method.

A Random Sampling-Based Method via Gaussian Process for Motion Planning in Dynamic Environments

Motion planning is widely applied to industrial robots, medical robots, bionic robots, and smart vehicles. Most work environments of robots are not static, which leads to difficulties for robot motion planning. We present a dynamic Gaussian local planner (DGLP) method to solve motion planning problems in dynamic environments. In a dynamic environment, dynamic obstacles sometimes make part of the global path invalid, so the local invalid path needs to be local re-planned online. Compared with the node sampling-based methods building large-scale random trees or roadmaps, the Gaussian random path sampling (GRPS) module integrated in the DGLP directly samples smooth random paths discretized into sparse nodes to improve the local path re-planning efficiency. We also provide the path end orientation constraint (PEOC) method for the local re-planning paths in order to merge them smoothly into the global paths. In the robot experiments, the average planning time of the DGLP is 0.04s, which is at least 92.31% faster than the test methods, and its comprehensive evaluation scores, which consider the consuming time, path quality, and success rate of local re-planning, are at least 44.92% higher than the test methods. The results demonstrate that the proposed DGLP method is able to efficiently provide high-quality local re-planning paths in dynamic environments.

An Efficient Motion Planning Method with a Lazy Demonstration Graph for Repetitive Pick-and-Place.

Robotic systems frequently need to plan consecutive similar manipulation in some scenarios (e.g., pick-and-place tasks), leading to similar motion plans. Moreover, the workspace of a robot changes with the difference in operation actions, which affects subsequent tasks. Therefore, it is significant to reuse information from previous solutions for new motion planning instances to adapt to workplace changes. This paper proposes the Lazy Demonstration Graph (LDG) planner, a novel motion planner that exploits successful and high-quality planning cases as prior knowledge. In addition, a Gaussian Mixture Model (GMM) is established by learning the distribution of samples in the planning cases. Through the trained GMM, more samples are placed in a promising location related to the planning tasks for achieving the purpose of adaptive sampling. This adaptive sampling strategy is combined with the Lazy Probabilistic Roadmap (LazyPRM) algorithm; in the subsequent planning tasks, this paper uses the multi-query property of a road map to solve motion planning problems without planning from scratch. The lazy collision detection of the LazyPRM algorithm helps overcome changes in the workplace by searching candidate paths. Our method also improves the quality and success rate of the path planning of LazyPRM. Compared with other state-of-the-art motion planning algorithms, our method achieved better performance in the planning time and path quality. In the repetitive motion planning experiment of the manipulator for pick-and-place tasks, we designed two different experimental scenarios in the simulation environment. The physical experiments are also carried out in AUBO-i5 robot arm. Accordingly, the experimental results verified our method's validity and robustness.

Research on the Behavioral Dynamics Motion Planning Method of the Human-Vehicle Social Force Model.

The interactive motion planning between unmanned vehicles and pedestrians in urban road environments is the key to realizing the autonomous motion of unmanned vehicles in hybrid traffic scenarios. The problem of human-vehicle interaction motion planning modeling at complex intersections is studied for an unmanned vehicle in this article. First, the motion planning of pedestrians and the unmanned vehicles is established according to the social force model and the behavioral dynamics model. Then, the autonomous vehicle is added to the crowd, and the human-vehicle interaction force is established. The virtual force is added to the social force model and the behavioral dynamics model, respectively, and the improved social force model and the behavioral dynamics model are used for the motion planning of pedestrians and unmanned vehicles. In this way, the established model solves the problems of simple pedestrian interaction motion planning in the social force model and single-body motion planning in the behavioral dynamics and thus provides a strong support for multibody motion planning. Finally, through the interactive motion planning trajectory of pedestrians and unmanned vehicles in different scenes, the vehicle and pedestrian motion planning trajectory can effectively avoid overlapping or crossing, so as to avoid the collision, which verifies the effectiveness and feasibility of the proposed model.

Robotic Motion Planning in Dynamic Environments and its Applications

The fundamental problem of robot motion planning in a dynamic environment (RMPDE) is to find an optimal collision-free path from the start to the goal in a dynamic environment. Our literature survey of over 100 papers from the last four decades reveals that there are more than 30 models of RMPDE, and there is no benchmarking criterion to select one that is the best in a given situation. In this context, generating a regression-based model with 10 attributes is the first and foremost contribution of our research. Given a highly human-interactive environment like a cafeteria or a bus stand, the gross hidden Markov model has special importance for modeling a robot path. A variant of the growing hidden Markov model for a serving robot in a cafeteria is the second contribution of this paper. We simulated the behavior of GHMM in a cafeteria with static and dynamic obstacles (static obstacles were both convex and concave) and with three different arrangements of the tables and obstacles. Robots have been employed in mushroom harvesting. A novel proposition discussed in this paper is probabilistic road map planning for a robot that finds an optimum path for reaching the ripened mushrooms in a randomly planted mushroom farm and a dexterous hand to pluck the selected mushrooms by employing inverse kinematics. Further, two biologically inspired meta-heuristic algorithms, ant colony optimization, and firefly has been studied for their application to latex collection. The simulation results with this environment show that the firefly algorithm outperforms ant colony optimization in the general case. Finally, we have proposed a few pointers for future research in this domain. The compilation and comparison of various approaches to robot motion planning in highly dynamic environments, and the simulation of a few models for some typical scenarios, have been the contributions of this paper.

Traction Adaptive Motion Planning and Control at the Limits of Handling

In this article, we address the problem of motion planning and control at the limits of handling, under locally varying traction conditions. We propose a novel solution method where traction variations over the prediction horizon are represented by time-varying tire force constraints, derived from a predictive friction estimate. A constrained finite time optimal control problem (CFTOC) is solved in a receding horizon fashion, imposing these time-varying constraints. Furthermore, our method features an integrated sampling augmentation procedure that addresses the problems of infeasibility and sensitivity to local minima that arise at abrupt constraint alterations, for example, due to sudden friction changes. We validate the proposed algorithm on a Volvo FH16 heavy-duty vehicle, in a range of critical scenarios. Experimental results indicate that traction adaptive motion planning and control improves the vehicle’s capacity to avoid accidents, both when adapting to low local traction, by ensuring dynamic feasibility of the planned motion, and when adapting to high local traction, by realizing high traction utilization.

Taylor Discrete Circadian Rhythms Neural Network for Resolving Bicriteria Optimization Problem of Redundant Robot Manipulators Perturbed by Periodic Noises

To solve the motion planning problems of redundant manipulators disturbed by the periodic noise from device hardwares or their surroundings, a Taylor-type discrete-time circadian rhythms neural network (TD-CRNN) method is proposed, developed, and studied in this article. First, a representative bicriteria optimization scheme combining torque criterion and acceleration criterion is presented for the redundant manipulator. Second, inspired by a continuous-time circadian rhythms model, the corresponding TD-CRNN model is derived based on the Taylor discrete formulation. Third, the 0-stability, convergence, and consistency of the proposed TD-CRNN model are analyzed theoretically and proved strictly. Finally, to confirm the capacity of the resisting periodic noise in the tracking problem of manipulators, two groups of comparative simulations and experiments conducted by the proposed TD-CRNN model are performed before the conclusion is given.

ИССЛЕДОВАНИЕ МЕТОДОВ ПЛАНИРОВАНИЯ ДВИЖЕНИЯ В ДВУМЕРНЫХ КАРТОГРАФИРОВАННЫХ СРЕДАХ

The article studies the problem of motion planning in two-dimensional mapped environments.The review and analysis of known planning algorithms based on Voronoi diagrams, probabilisticroad maps, rapidly growing random trees, Dijkstra algorithms, A*, D* and their modifications, artificialpotential fields and intelligent heuristics are carried out. Based on the analysis, it is concludedthat classical methods in dynamic environments require significant costs in terms of calculation timeand the amount of memory used. The conclusion is made about the relevance of the development ofalgorithms that increase the efficiency of known planning methods. In this regard, this article is devotedto the development of a modified algorithm of rapidly growing random trees and the study of itseffectiveness in comparison with known methods. The article presents a modified algorithm for rapidlygrowing random trees, characterized in that when checking for a path to a new potential node ofthe tree, the path to some area near the specified node is checked. This reduces the number of nodesin the tree under construction. The developed algorithm is first compared with the traditional algorithmof fast-growing random trees. The comparison is made by the trajectory calculation time, theamount of memory required, the path length and the percentage of situations in which the trajectoryto the target point was successfully found. Next, the developed algorithm is compared with the planningalgorithms of other classes. The study uses representative samples of numerical experiments andvarious environments that differ in the density of obstacles and the presence of mazes. A study ofplanning algorithms using the results of experiments on a ground-based wheeled robot is also beingconducted. Based on the results of numerical and real experiments, conclusions are drawn about theadvantages and disadvantages of the developed algorithm of motion planning and the feasibility of itsapplication in various environments.

Motion planning for a high order Dubins vehicle

AbstractIn this paper, we focus on the motion planning problem (MPP) of a generalized Dubins vehicle (GDV) with higher order dynamics, aiming at mitigating the drawbacks caused by the lack of smoothness of the Dubins curves. In the two‐dimensional case, the MPP is converted, by exploiting the Pontryagin maximum principle, into the problem of solving a set of algebraic equations (AEs). The solution of the set of AEs, which can also be applied to the MPP of chained‐form and flat systems, is found by systematically using the concept of elementary symmetric polynomial. Furthermore, in extending our results to the three‐dimensional case, the explicit expression of a new class of space curves is obtained using the Frenet frame. Simulation results show the superiority of the curves generated by the GDV over that generated by the conventional Dubins vehicle.