Collision-free motion planning for two articulated robot arms using minimum distance functions

Robotica ◽  
1990 ◽  
Vol 8 (2) ◽  
pp. 137-144 ◽  
Author(s):  
C. Chang ◽  
M. J. Chung ◽  
Z. Bien
Keyword(s):  
Motion Planning ◽  
Minimum Distance ◽  
Three Dimensional ◽  
Distance Functions ◽  
Free Motion ◽  
Planning Problem ◽  
Robot Arm ◽  
Robot Arms ◽  
Nonlinear Minimization ◽  
Articulated Robot

SummaryThis paper presents a collision-free motion planning method of two articulated robot arms in a three dimensional common work space. Each link of a robot arm is modeled by a cylinder ended by two hemispheres, and the remaining wrist and hand is modeled by a sphere. To describe the danger of collision between two modeled objects, minimum distance functions, which are defined by the Euclidean norm, are used. These minimum distance functions are used to describe the constraints that guarantee no collision between two robot arms. The collision-free motion planning problem is formulated as a pointwise constrained nonlinear minimization problem, and solved by a conjugate gradient method with barrier functions. To improve the minimization process, a simple grid technique is incorporated. Finally, a simulation study is presented to show the significance of the proposed method.

scholarly journals Contact-Rich Trajectory Generation in Confined Environments Using Iterative Convex Optimization

2020 ◽  
Author(s):  
Wei-Ye Zhao ◽  
Suqin He ◽  
Chengtao Wen ◽  
Changliu Liu
Keyword(s):  
Convex Optimization ◽  
Motion Planning ◽  
Real Time ◽  
Trajectory Generation ◽  
Robot Kinematics ◽  
Planning Problem ◽  
Robot Arm ◽  
Task Constraints ◽  
Robot Arms ◽  
Highly Nonlinear

Abstract Applying intelligent robot arms in dynamic uncertain environments (i.e., flexible production lines) remains challenging, which requires efficient algorithms for real time trajectory generation. The motion planning problem for robot trajectory generation is highly nonlinear and nonconvex, which usually comes with collision avoidance constraints, robot kinematics and dynamics constraints, and task constraints (e.g., following a Cartesian trajectory defined on a surface and maintain the contact). The nonlinear and nonconvex planning problem is computationally expensive to solve, which limits the application of robot arms in the real world. In this paper, for redundant robot arm planning problems with complex constraints, we present a motion planning method using iterative convex optimization that can efficiently handle the constraints and generate optimal trajectories in real time. The proposed planner guarantees the satisfaction of the contact-rich task constraints and avoids collision in confined environments. Extensive experiments on trajectory generation for weld grinding are performed to demonstrate the effectiveness of the proposed method and its applicability in advanced robotic manufacturing.

Computer Aided Synthesis of Piecewise Rational Motions for Spherical 2R and 3R Robot Arms

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Anurag Purwar ◽  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Motion Planning ◽  
Spline Interpolation ◽  
Robot Arm ◽  
Spherical Robot ◽  
Kinematic Constraints ◽  
Robot Arms ◽  
Revolute Joints ◽  
Computer Aided ◽  
Planar Robot ◽  
Circular Interpolation

This paper deals with the problem of synthesizing smooth piecewise rational spherical motions of an object that satisfies the kinematic constraints imposed by a spherical robot arm with revolute joints. This paper brings together the kinematics of spherical robot arms and recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. The kinematic constraints under consideration are workspace related constraints that limit the orientation of the end link of robot arms. This paper extends our previous work on synthesis of rational motions under the kinematic constraints of planar robot arms. Using quaternion kinematics of spherical arms, it is shown that the problem of synthesizing the Cartesian rational motion of a 2R arm can be reduced to that of circular interpolation in two separate planes. Furthermore, the problem of synthesizing the Cartesian rational motion of a spherical 3R arm can be reduced to that of constrained spline interpolation in two separate planes. We present algorithms for the generation of C1 and C2 continuous rational motion of spherical 2R and 3R robot arms.

Computer Aided Synthesis of Piecewise Rational Motions for Planar 2R and 3R Robot Arms

2006 ◽  
Vol 129 (10) ◽  
pp. 1031-1036 ◽  
Author(s):  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Motion Planning ◽  
Spline Interpolation ◽  
Circular Ring ◽  
Robot Arm ◽  
Kinematic Constraints ◽  
Robot Arms ◽  
Revolute Joints ◽  
Computer Aided ◽  
Planar Robot ◽  
Circular Interpolation

This paper deals with the problem of synthesizing piecewise rational motions of an object that satisfies kinematic constraints imposed by a planar robot arm with revolute joints. This paper brings together the kinematics of planar robot arms and the recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. Through the use of planar quaternions, it is shown that for the case of a planar 2R arm, the problem of rational motion synthesis can be reduced to that of circular interpolations in two separate planes and that for the case of a planar 3R arm, the problem can be reduced to a combination of circular interpolation in one plane and a constrained spline interpolation in a circular ring on another plane. Due to the limitation of circular interpolation, only C1 continuous rational motions are generated that satisfy the kinematic constraints exactly. For applications that require C2 continuous motions, this paper presents a method for generating C2 continuous motions that approximate the kinematic constraints for planar 2R and 3R robot arms.

Obstacle Avoidance Influence Coefficients for Manipulator Motion Planning

2005 ◽  
Author(s):  
Troy Harden ◽  
Chetan Kapoor ◽  
Delbert Tesar
Keyword(s):  
Motion Planning ◽  
Obstacle Avoidance ◽  
Minimum Distance ◽  
Higher Order ◽  
Second Order ◽  
Distance Functions ◽  
Cluttered Environments ◽  
Finite Difference Approximations ◽  
Planning Decisions ◽  
Influence Coefficients

Motion planning in cluttered environments is a weakness of current robotic technology. While research addressing this issue has been conducted, few efforts have attempted to use minimum distance rates of change in motion planning. Geometric influence coefficients provide extraordinary insight into the interactions between a robot and its environment. They isolate the geometry of distance functions from system inputs and make the higher-order properties of minimum distance magnitudes directly available. Knowledge of the higher order properties of minimum distance magnitudes can be used to predict the future obstacle avoidance, path planning, and/or target acquisition state of a manipulator system and aid in making intelligent motion planning decisions. Here, first and second order geometric influence coefficients for minimum distance magnitudes are rigorously developed for several simple modeling primitives. A general method for similar derivations using new primitives and an evaluation of finite difference approximations versus analytical second order coefficient calculations are presented. Two application examples demonstrate the utility of minimum distance magnitude influence coefficients in motion planning.

scholarly journals Multiquery Motion Planning in Uncertain Spaces: Incremental Adaptive Randomized Roadmaps

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.

Choice of Muscular Forces for Motion Control of a Robot Arm with Biarticular Muscles

2019 ◽  
Vol 31 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Tetsuya Morizono ◽  
Kenji Tahara ◽  
Hitoshi Kino ◽  
◽  
Keyword(s):  
Motion Control ◽  
Robot Arm ◽  
Joint Torques ◽  
Moment Arms ◽  
Robot Arms ◽  
Biarticular Muscles ◽  
Kinetic Interaction ◽  
Simulation Results ◽  
Articulated Robot ◽  
Point To Point

The contribution of biarticular muscles to the control of robotic arms and legs has recently attracted great interest in the field of robotics. The advantages of using biarticular muscles under kinetic interaction with the external environment have been well studied; however, the contribution of the muscles to the motion control of articulated robot arms under no kinetic interaction appears to remain an unclear issue, especially for robot arms of which the muscles are directly anchored to their links, which induces a change in the moment arms to allow the muscles to generate joint torques and permit point-to-point motion control to their desired postures in a feedforward manner with constant muscular forces. This paper presents a case study in which the role of biarticular muscles in the motion control of an articulated robot arm was investigated, focusing on the feature of its redundancy actuation, which allows an arbitrary choice from infinite combinations of muscular forces, realizing motion control to a desired posture. The numerical analysis in this paper addresses three typical combination choices. Mappings from muscular forces to desired postures are calculated in the analysis of the three choices. The simulation results of motion control executed according to the three mappings are also analyzed. The analysis indicates the interesting results that biarticular muscles do not contribute to the desired postures and that a very weak dependence property of monoarticular muscles on the desired postures exists for a particular choice. The simulation results also demonstrate that the implementation of one choice results in a degraded motion control performance as compared with that of the two other choices.

Motion planning and trajectory tracking for three-dimensional Poiseuille flow

2009 ◽  
Vol 626 ◽  
pp. 307-332 ◽  
Author(s):  
JENNIE COCHRAN ◽  
MIROSLAV KRSTIC
Keyword(s):  
Motion Planning ◽  
Performance Metrics ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Independent Solution ◽  
Planning Problem ◽  
Reference Trajectory ◽  
Special Role ◽  
Motion Planning Problem

We present the first solution to a boundary motion planning problem for the Navier–Stokes equations, linearized around the parabolic equilibrium in a three-dimensional channel flow. The pressure and skin friction at one wall are chosen as the reference outputs as they are the most readily measurable ‘wall-restricted’ quantities in experimental fluid dynamics and also because they play a special role as performance metrics in aerodynamics. The reference velocity input is applied at the opposite wall. We find the exact (method independent) solution to the motion planning problem using the PDE (partial differential equation) backstepping theory. The motion planning solution results in open-loop controls, which produce the reference output trajectories only under special initial conditions for the flow velocity field. To achieve convergence to the reference trajectory from other (nearby) initial conditions, we design a feedback controller. We also present a detailed examination of the closed-form solutions for gains and the behaviour of the motion planning solution as the wavenumbers grow or the Reynolds number grows. Numerical results are shown for the motion planning problem.

MASSIVELY PARALLEL IDA* SEARCH

1993 ◽  
Vol 02 (02) ◽  
pp. 163-180 ◽  
Author(s):  
DIANE J. COOK ◽  
GARY LYONS
Keyword(s):  
Artificial Intelligence ◽  
Motion Planning ◽  
Heuristic Search ◽  
Massively Parallel ◽  
Search Process ◽  
Planning Problem ◽  
Robot Arm ◽  
Speed Up ◽  
Arm Motion ◽  
Computational Bottleneck

Heuristic search is a fundamental component of Artificial Intelligence applications. Because search routines are frequently also a computational bottleneck, numerous methods have been explored to increase the efficiency of search. Recently, researchers have begun investigating methods of using parallel MIMD and SIMD hardware to speed up the search process. In this paper, we present a massively-parallel SIMD approach to search named MIDA* search. The components of MIDA* include a very fast distribution algorithm which biases the search to one side of the tree, and an incrementally-deepening depthfirst search of all the processors in parallel. We show the results of applying MIDA* to instances of the Fifteen Puzzle problem and to the robot arm motion planning problem. Results reveal an efficiency of 74% and a speedup of 8553 and 492 over serial and 16-processor MIMD algorithms, respectively, when finding a solution to the Fifteen Puzzle problem that is close to optimal.

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