A continuation method for motion-planning problems

Automated motion-planning technologies for industrial robots are critical for their application to Industry 4.0. Various sampling-based methods have been studied to generate the collision-free motion of articulated industrial robots. Such sampling-based methods provide efficient solutions to complex planning problems, but their limitations hinder the attainment of optimal results. This paper considers a method to obtain the optimal results in the roadmap algorithm that is representative of the sampling-based method. We define the coverage of a graph as a performance index of its optimality as constructed by a sampling-based algorithm and propose an optimization algorithm that can maximize graph coverage in the configuration space. The proposed method was applied to the model of an industrial robot, and the results of the simulation confirm that the roadmap graph obtained by the proposed algorithm can generate results of satisfactory quality in path-finding tests under various conditions.

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Tangent bundle RRT: A randomized algorithm for constrained motion planning

Robotica ◽

10.1017/s0263574714001234 ◽

2014 ◽

Vol 34 (1) ◽

pp. 202-225 ◽

Cited By ~ 29

Author(s):

Beobkyoon Kim ◽

Terry Taewoong Um ◽

Chansu Suh ◽

F. C. Park

Keyword(s):

Motion Planning ◽

Configuration Space ◽

Tangent Bundle ◽

Numerical Experiments ◽

Randomized Algorithm ◽

Random Trees ◽

Constrained Motion ◽

Wide Range ◽

Random Node ◽

Planning Problems

SUMMARYThe Tangent Bundle Rapidly Exploring Random Tree (TB-RRT) is an algorithm for planning robot motions on curved configuration space manifolds, in which the key idea is to construct random trees not on the manifold itself, but on tangent bundle approximations to the manifold. Curvature-based methods are developed for constructing tangent bundle approximations, and procedures for random node generation and bidirectional tree extension are developed that significantly reduce the number of projections to the manifold. Extensive numerical experiments for a wide range of planning problems demonstrate the computational advantages of the TB-RRT algorithm over existing constrained path planning algorithms.

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Multiquery Motion Planning in Uncertain Spaces: Incremental Adaptive Randomized Roadmaps

International Journal of Applied Mathematics and Computer Science ◽

10.2478/amcs-2019-0047 ◽

2019 ◽

Vol 29 (4) ◽

pp. 641-654

Author(s):

Weria Khaksar ◽

Md Zia Uddin ◽

Jim Torresen

Keyword(s):

Motion Planning ◽

Minimum Distance ◽

Planning Problem ◽

Grid Structure ◽

Discrete Time System ◽

Environment Map ◽

Sample Classification ◽

Adjustment Strategy ◽

Hybrid Sample ◽

Planning Problems

Abstract Sampling-based motion planning is a powerful tool in solving the motion planning problem for a variety of different robotic platforms. As its application domains grow, more complicated planning problems arise that challenge the functionality of these planners. One of the main challenges in the implementation of a sampling-based planner is its weak performance when reacting to uncertainty in robot motion, obstacles motion, and sensing noise. In this paper, a multi-query sampling-based planner is presented based on the optimal probabilistic roadmaps algorithm that employs a hybrid sample classification and graph adjustment strategy to handle diverse types of planning uncertainty such as sensing noise, unknown static and dynamic obstacles and an inaccurate environment map in a discrete-time system. The proposed method starts by storing the collision-free generated samples in a matrix-grid structure. Using the resulting grid structure makes it computationally cheap to search and find samples in a specific region. As soon as the robot senses an obstacle during the execution of the initial plan, the occupied grid cells are detected, relevant samples are selected, and in-collision vertices are removed within the vision range of the robot. Furthermore, a second layer of nodes connected to the current direct neighbors are checked against collision, which gives the planner more time to react to uncertainty before getting too close to an obstacle. The simulation results for problems with various sources of uncertainty show a significant improvement compared with similar algorithms in terms of the failure rate, the processing time and the minimum distance from obstacles. The planner is also successfully implemented and tested on a TurtleBot in four different scenarios with uncertainty.

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Sampling-based methods for factored task and motion planning

The International Journal of Robotics Research ◽

10.1177/0278364918802962 ◽

2018 ◽

Vol 37 (13-14) ◽

pp. 1796-1825 ◽

Cited By ~ 7

Author(s):

Caelan Reed Garrett ◽

Tomás Lozano-Pérez ◽

Leslie Pack Kaelbling

Keyword(s):

Motion Planning ◽

General Purpose ◽

State Transitions ◽

Transition Systems ◽

Hybrid State ◽

Time Planning ◽

And Control ◽

Planning Problems ◽

Domain Independent

This paper presents a general-purpose formulation of a large class of discrete-time planning problems, with hybrid state and control-spaces, as factored transition systems. Factoring allows state transitions to be described as the intersection of several constraints each affecting a subset of the state and control variables. Robotic manipulation problems with many movable objects involve constraints that only affect several variables at a time and therefore exhibit large amounts of factoring. We develop a theoretical framework for solving factored transition systems with sampling-based algorithms. The framework characterizes conditions on the submanifold in which solutions lie, leading to a characterization of robust feasibility that incorporates dimensionality-reducing constraints. It then connects those conditions to corresponding conditional samplers that can be composed to produce values on this submanifold. We present two domain-independent, probabilistically complete planning algorithms that take, as input, a set of conditional samplers. We demonstrate the empirical efficiency of these algorithms on a set of challenging task and motion planning problems involving picking, placing, and pushing.

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An Approach to Dynamic Distance Calculations for Obstacle Avoidance Problems

3rd Conference on Flexible Assembly Systems ◽

10.1115/detc1991-0165 ◽

1991 ◽

Author(s):

C. Y. Liu ◽

W. R. Chen ◽

R. W. Mayne

Keyword(s):

Motion Planning ◽

Calculation Method ◽

Two Dimensional ◽

Robot Path Planning ◽

Distance Calculation ◽

Approach Distance ◽

Quadratic Programming Method ◽

Swept Volume ◽

Planning Problems ◽

Robot Path

Abstract This paper presents a distance calculation method which can be used in machine motion planning optimizations where interference is a concern. Dynamic distance calculations are discussed which use the quadratic programming method combined with an approximate swept volume approach. Distance-to-contact calculations can be obtained for both interference and non-interference situations. The swept volume of a moving polygon is constructed through a series of overlapped swept volume segments. Each of the swept volume segments is efficiently developed by checking the inner products of polygon outward boundary normals with velocity vectors for polygon vertices. Two dimensional examples of distance-to-contact computations and robot path planning problems are presented for a sample three link robot with three rotational joints.

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Continuous-time Gaussian process motion planning via probabilistic inference

The International Journal of Robotics Research ◽

10.1177/0278364918790369 ◽

2018 ◽

Vol 37 (11) ◽

pp. 1319-1340 ◽

Cited By ~ 16

Author(s):

Mustafa Mukadam ◽

Jing Dong ◽

Xinyan Yan ◽

Frank Dellaert ◽

Byron Boots

Keyword(s):

Motion Planning ◽

Gaussian Process ◽

Continuous Time ◽

Trajectory Optimization ◽

Probabilistic Inference ◽

Incremental Algorithm ◽

Factor Graph ◽

Gradient Based ◽

Time Required ◽

Planning Problems

We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian process (GP) models. We next develop an efficient gradient-based optimization algorithm that exploits this sparsity and GP interpolation. We call this algorithm the Gaussian Process Motion Planner (GPMP). We then detail how motion planning problems can be formulated as probabilistic inference on a factor graph. This forms the basis for GPMP2, a very efficient algorithm that combines GP representations of trajectories with fast, structure-exploiting inference via numerical optimization. Finally, we extend GPMP2 to an incremental algorithm, iGPMP2, that can efficiently replan when conditions change. We benchmark our algorithms against several sampling-based and trajectory optimization-based motion planning algorithms on planning problems in multiple environments. Our evaluation reveals that GPMP2 is several times faster than previous algorithms while retaining robustness. We also benchmark iGPMP2 on replanning problems, and show that it can find successful solutions in a fraction of the time required by GPMP2 to replan from scratch.

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