scholarly journals Development of Task-Space Nonholonomic Motion Planning Algorithm Based on Lie-Algebraic Method

2021 ◽  
Vol 11 (21) ◽  
pp. 10245
Author(s):  
Arkadiusz Mielczarek ◽  
Ignacy Dulęba
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Algebraic Method ◽  
Nonholonomic Systems ◽  
Inverse Kinematic ◽  
General Purpose ◽  
Task Space ◽  
Local Motion ◽  
Planning Algorithm ◽  
Nonholonomic Motion Planning

In this paper, a Lie-algebraic nonholonomic motion planning technique, originally designed to work in a configuration space, was extended to plan a motion within a task-space resulting from an output function considered. In both planning spaces, a generalized Campbell–Baker–Hausdorff–Dynkin formula was utilized to transform a motion planning into an inverse kinematic task known for serial manipulators. A complete, general-purpose Lie-algebraic algorithm is provided for a local motion planning of nonholonomic systems with or without output functions. Similarities and differences in motion planning within configuration and task spaces were highlighted. It appears that motion planning in a task-space can simplify a planning task and also gives an opportunity to optimize a motion of nonholonomic systems. Unfortunately, in this planning there is no way to avoid working in a configuration space. The auxiliary objective of the paper is to verify, through simulations, an impact of initial parameters on the efficiency of the planning algorithm, and to provide some hints on how to set the parameters correctly.

scholarly journals A sampling-based optimized algorithm for task-constrained motion planning

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141984737 ◽  
Author(s):  
Kai Mi ◽  
Haojian Zhang ◽  
Jun Zheng ◽  
Jianhua Hu ◽  
Dengxiang Zhuang ◽  
...  
Keyword(s):  
Motion Planning ◽  
Sampling Methods ◽  
Tracking Error ◽  
Joint Space ◽  
Planning Problem ◽  
Redundant Manipulators ◽  
Task Space ◽  
Constrained Motion ◽  
Smooth Path ◽  
Planning Algorithm

We consider a motion planning problem with task space constraints in a complex environment for redundant manipulators. For this problem, we propose a motion planning algorithm that combines kinematics control with rapidly exploring random sampling methods. Meanwhile, we introduce an optimization structure similar to dynamic programming into the algorithm. The proposed algorithm can generate an asymptotically optimized smooth path in joint space, which continuously satisfies task space constraints and avoids obstacles. We have confirmed that the proposed algorithm is probabilistically complete and asymptotically optimized. Finally, we conduct multiple experiments with path length and tracking error as optimization targets and the planning results reflect the optimization effect of the algorithm.

scholarly journals Inverse kinematics-based motion planning for dual-arm robot with orientation constraints

2019 ◽  
Vol 16 (2) ◽  
pp. 172988141983685 ◽  
Author(s):  
Jiangping Wang ◽  
Shirong Liu ◽  
Botao Zhang ◽  
Changbin Yu
Keyword(s):  
Motion Planning ◽  
Joint Space ◽  
Inverse Kinematic ◽  
Planning Problem ◽  
Constraint Manifold ◽  
Wide Range ◽  
Planning Algorithm ◽  
Motion Paths ◽  
Dual Arm Robot ◽  
Dual Arm

This article proposes an efficient and probabilistic complete planning algorithm to address motion planning problem involving orientation constraints for decoupled dual-arm robots. The algorithm is to combine sampling-based planning method with analytical inverse kinematic calculation, which randomly samples constraint-satisfying configurations on the constraint manifold using the analytical inverse kinematic solver and incrementally connects them to the motion paths in joint space. As the analytical inverse kinematic solver is applied to calculate constraint-satisfying joint configurations, the proposed algorithm is characterized by its efficiency and accuracy. We have demonstrated the effectiveness of our approach on the Willow Garage’s PR2 simulation platform by generating trajectory across a wide range of orientation-constrained scenarios for dual-arm manipulation.

scholarly journals A Fast Evaluation of Initial Configurations in Repeatable Inverse Kinematics for Redundant Manipulators

2018 ◽  
Vol 28 (3) ◽  
pp. 483-492
Author(s):  
Ignacy Duleba ◽  
Iwona Karcz-Duleba ◽  
Arkadiusz Mielczarek
Keyword(s):  
Configuration Space ◽  
Inverse Kinematics ◽  
Indirect Method ◽  
Inverse Kinematic ◽  
Initial Configuration ◽  
Redundant Manipulators ◽  
Task Space ◽  
Original Function ◽  
Fast Evaluation ◽  
Computationally Expensive

Abstract A repeatable inverse kinematic task in robot manipulators consists in finding a loop (cyclic trajectory) in a configuration space, which corresponds to a given loop in a task space. In the robotic literature, an entry configuration to the trajectory is fixed and given by a user. In this paper the assumption is released and a new, indirect method is introduced to find entry configurations generating short trajectories. The method avoids a computationally expensive evaluation of (infinite) many entry configurations for redundant manipulators (for each of them, repeatable inverse kinematics should be run). Some fast-to-compute functions are proposed to evaluate entry configurations and their correlations with resulting lengths of trajectories are computed. It appears that only an original function, based on characteristics of a manipulability subellipsoid, properly distinguishes entry configurations that generate short trajectories. This function can be used either to choose one from a few possible entry configurations or as an optimized function to compute the best initial configuration.

An Efficient Path-Planning Algorithm for a Robotic Manipulator by Automatic Selection Search of Indispensable Regions in Its Configuration Space

1992 ◽  
Vol 4 (5) ◽  
pp. 378-385
Author(s):  
Hiroshi Noborio ◽  
◽  
Motohiko Watanabe ◽  
Takeshi Fujii
Keyword(s):  
Path Planning ◽  
Motion Planning ◽  
Configuration Space ◽  
Robotic Manipulator ◽  
Joint Space ◽  
Practical Applications ◽  
Continuous Sequence ◽  
Angle Difference ◽  
Planning Algorithm ◽  
Path Planning Algorithm

In this paper, we propose a feasible motion planning algorithm for a robotic manipulator and its obstacles. The algorithm quickly selects a feasible sequence of collision-free motions while adaptively expanding a graph in the implicit configuration joint-space. In the configuration graph, each arc represents an angle difference of the manipulator joint; therefore, an arc sequence represents a continuous sequence of robot motions. Thus, the algorithm can execute a continuous sequence of collision-free motions. Furthermore, the algorithm expands the configuration graph only in space which is to be cluttered in the implicit configuration joint-space and which is needed to select a collision-free sequence between the initial and target positions/orientations. The algorithm maintains the configuration graph in a small size and quickly selects a collision-free sequence from the configuration graph, whose shape is to be simple enough to move the manipulator in practical applications.

Layer, Lie algebraic method of motion planning for nonholonomic systems

2012 ◽  
Vol 349 (1) ◽  
pp. 201-215 ◽  
Author(s):  
Ignacy Duleba ◽  
Wissem Khefifi ◽  
Iwona Karcz-Duleba
Keyword(s):  
Motion Planning ◽  
Algebraic Method ◽  
Nonholonomic Systems

scholarly journals Exploring implicit spaces for constrained sampling-based planning

2019 ◽  
Vol 38 (10-11) ◽  
pp. 1151-1178 ◽  
Author(s):  
Zachary Kingston ◽  
Mark Moll ◽  
Lydia E Kavraki
Keyword(s):  
Motion Planning ◽  
Open Source ◽  
Configuration Space ◽  
Broad Class ◽  
Asymptotic Optimality ◽  
Configuration Spaces ◽  
Local Planning ◽  
Planning Algorithm

We present a review and reformulation of manifold constrained sampling-based motion planning within a unifying framework, IMACS (implicit manifold configuration space). IMACS enables a broad class of motion planners to plan in the presence of manifold constraints, decoupling the choice of motion planning algorithm and method for constraint adherence into orthogonal choices. We show that implicit configuration spaces defined by constraints can be presented to sampling-based planners by addressing two key fundamental primitives, sampling and local planning, and that IMACS preserves theoretical properties of probabilistic completeness and asymptotic optimality through these primitives. Within IMACS, we implement projection- and continuation-based methods for constraint adherence, and demonstrate the framework on a range of planners with both methods in simulated and realistic scenarios. Our results show that the choice of method for constraint adherence depends on many factors and that novel combinations of planners and methods of constraint adherence can be more effective than previous approaches. Our implementation of IMACS is open source within the Open Motion Planning Library and is easily extended for novel planners and constraint spaces.

A real-time motion planning algorithm for a hyper-redundant set of mechanisms

Robotica ◽  
2013 ◽  
Vol 31 (8) ◽  
pp. 1327-1335 ◽  
Author(s):  
Nir Shvalb ◽  
Boaz Ben Moshe ◽  
Oded Medina
Keyword(s):  
Motion Planning ◽  
Real Time ◽  
Configuration Space ◽  
Degrees Of Freedom ◽  
Morse Function ◽  
Climbing Robot ◽  
Probabilistic Algorithm ◽  
Road Map ◽  
Time Motion ◽  
Planning Algorithm

SUMMARYWe introduce a novel probabilistic algorithm (CPRM) for real-time motion planning in the configuration space${\EuScript C}$. Our algorithm differs from a probabilistic road map (PRM) algorithm in the motion between a pair of anchoring points (local planner) which takes place on the boundary of the obstacle subspace${\EuScript O}$. We define a varying potential fieldfon ∂${\EuScript O}$as a Morse function and follow$\vec{\nabla} f$. We then exemplify our algorithm on a redundant worm climbing robot withndegrees of freedom and compare our algorithm running results with those of the PRM.

A Surface Integral Approach to the Motion Planning of Nonholonomic Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 315-325 ◽  
Author(s):  
Ranjan Mukherjee ◽  
David P. Anderson
Keyword(s):  
Motion Planning ◽  
Surface Area ◽  
Configuration Space ◽  
Degrees Of Freedom ◽  
Nonholonomic Systems ◽  
Integral Approach ◽  
Surface Integral ◽  
Independent Variables ◽  
Dependent Variables ◽  
Disk Rolling

Nonholonomic mechanical systems are governed by constraints of motion that are nonintegrable differential expressions. Unlike holonomic constraints, these constraints do not reduce the number of dimensions of the configuration space of a system. Therefore a nonholonomic system can access a configuration space of dimension higher than the number of the degrees of freedom of the system. In this paper, we develop an algorithm for planning admissible trajectories for nonholonomic systems that will take the system from one point in its configuration space to another. In our algorithm the independent variables are first converged to their desired values. Subsequently, closed trajectories of the independent variables are used to converge the dependent variables. We use Green’s theorem in our algorithm to convert the problem of finding a closed path into that of finding a surface area in the space of the independent variables such that the dependent variables converge to their desired values as the independent variables traverse along the boundary of this surface area. Using this approach, we specifically address issues related to the reachability of the system, motion planning amidst additional constraints, and repeatable motion of nonholonomic systems. The salient features of our algorithm are quite apparent in the two examples we discuss: a planar space robot and a disk rolling without slipping on a flat surface.

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