IMPLICIT POINT LOCATION IN ARRANGEMENTS OF LINE SEGMENTS, WITH AN APPLICATION TO MOTION PLANNING

1994 ◽  
Vol 04 (04) ◽  
pp. 369-383
Author(s):  
PANKAJ K. AGARWAL ◽  
MARC VAN KREVELD
Keyword(s):  
Data Structure ◽  
Motion Planning ◽  
Location Problem ◽  
Translational Motion ◽  
Planning Problem ◽  
Final Position ◽  
Point Location ◽  
Line Segments ◽  
Planar Region ◽  
The Face

Let [Formula: see text] be a set of n (possibly intersecting) line segments in the plane. We show that the arrangement of [Formula: see text] can be stored implicitly in a data structure of size O(n log 2n) so that the following query can be answered in time O(n1/2 log 2 n): Given two query points, determine whether they lie in the same face of the arrangement of S and, if so, return a path between them that lies within the face. This version of the implicit point location problem is motivated by the following motion planning problem: Given a polygonal robot R with m vertices and a planar region bounded by polygonal obstacles with n vertices in total, preprocess them into a data structure so that, given initial and final positions of R, one can quickly determine whether there exists a continuous collision-free translational motion of R from the initial to the final position. We show that such a query can be answered in time O((mn)1/2 log 2 mn) using O(mn log 2 mn) storage.

Motion Planning for a Spherical Mobile Robot: Revisiting the Classical Ball-Plate Problem

2002 ◽  
Vol 124 (4) ◽  
pp. 502-511 ◽  
Author(s):  
Ranjan Mukherjee ◽  
Mark A. Minor ◽  
Jay T. Pukrushpan
Keyword(s):  
Motion Planning ◽  
Kinematic Model ◽  
Parallel Transport ◽  
Planning Problem ◽  
Stabilizing Controller ◽  
Line Segments ◽  
Planning And Control ◽  
Hazardous Environments ◽  
Straight Line ◽  
Spherical Mobile Robot

In comparison to wheeled robots, spherical mobile robots offer greater mobility, stability, and scope for operation in hazardous environments. Inspite of these advantages, spherical designs have failed to gain popularity due to complexity of their motion planning and control problems. In this paper, we address the motion planning problem for the rolling sphere, often referred in the literature as the “ball-plate problem,” and propose two different algorithms for reconfiguration. The first algorithm, based on simple geometry, uses a standard kinematic model and invokes alternating inputs to obtain a solution comprised of circular arcs and straight line segments. The second algorithm is based on the Gauss-Bonet theorem of parallel transport and achieves reconfiguration through spherical triangle maneuvers. While the second algorithm is inherently simple and provides a solution comprised of straight line segments only, the first algorithm provides the basis for development of a stabilizing controller. Our stabilizing controller, which will be presented in our next paper, will be the first solution to a problem that has eluded many researchers since the kinematic model of the sphere cannot be converted to chained form. Both our algorithms require numerical computation of a small number of parameters and provide the scope for easy implementation.

scholarly journals Normal form approach in the motion planning of space robots: a case study

2021 ◽  
Author(s):  
Krzysztof Tchoń ◽  
Katarzyna Zadarnowska
Keyword(s):  
Normal Form ◽  
Motion Planning ◽  
Normal Forms ◽  
Inverse Dynamics ◽  
Planning Problem ◽  
Inverse Dynamics Problem ◽  
Velocity Level ◽  
Form Approach ◽  
Space Approach

AbstractWe examine applicability of normal forms of non-holonomic robotic systems to the problem of motion planning. A case study is analyzed of a planar, free-floating space robot consisting of a mobile base equipped with an on-board manipulator. It is assumed that during the robot’s motion its conserved angular momentum is zero. The motion planning problem is first solved at velocity level, and then torques at the joints are found as a solution of an inverse dynamics problem. A novelty of this paper lies in using the chained normal form of the robot’s dynamics and corresponding feedback transformations for motion planning at the velocity level. Two basic cases are studied, depending on the position of mounting point of the on-board manipulator. Comprehensive computational results are presented, and compared with the results provided by the Endogenous Configuration Space Approach. Advantages and limitations of applying normal forms for robot motion planning are discussed.

Motion Planning of a Nonholonomic Multibody System Using Genetic Algorithm

2003 ◽  
Author(s):  
Xin-Sheng Ge ◽  
Li-Qun Chen
Keyword(s):  
Genetic Algorithm ◽  
Motion Planning ◽  
Nonholonomic System ◽  
Multibody System ◽  
Planning Problem ◽  
Control Approach ◽  
Velocity Constraints ◽  
Nonholonomic Motion Planning ◽  
Optimal Control Approach ◽  
Motion Planning Problem

The motion planning problem of a nonholonomic multibody system is investigated. Nonholonomicity arises in many mechanical systems subject to nonintegrable velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the control problem of system can be converted to the motion planning problem for a driftless control system. In this paper, we propose an optimal control approach for nonholonomic motion planning. The genetic algorithm is used to optimize the performance of motion planning to connect the initial and final configurations and to generate a feasible trajectory for a nonholonomic system. The feasible trajectory and its control inputs are searched through a genetic algorithm. The effectiveness of the genetic algorithm is demonstrated by numerical simulation.

Motion planning problem with obstacle avoidance for step-2 bracket-generating systems

PAMM ◽  
2017 ◽  
Vol 17 (1) ◽  
pp. 799-800 ◽  
Author(s):  
Victoria Grushkovskaya ◽  
Alexander Zuyev
Keyword(s):  
Motion Planning ◽  
Obstacle Avoidance ◽  
Planning Problem ◽  
Motion Planning Problem

scholarly journals Efficient Planning of Humanoid Motions by Modifying Constraints

2013 ◽  
Vol 4 (1) ◽  
Author(s):  
ChangHyun Sung ◽  
Takahiro Kagawa ◽  
Yoji Uno
Keyword(s):  
Motion Planning ◽  
Sufficient Conditions ◽  
Computation Time ◽  
Humanoid Robots ◽  
Body Motion ◽  
Whole Body ◽  
Planning Problem ◽  
Point Representation ◽  
Efficient Planning ◽  
Unpredictable Environment

AbstractIn this paper, we propose an effective planning method for whole-body motions of humanoid robots under various conditions for achieving the task. In motion planning, various constraints such as range of motion have to be considered. Specifically, it is important to maintain balance in whole-body motion. In order to be useful in an unpredictable environment, rapid planning is an essential problem. In this research, via-point representation is used for assigning sufficient conditions to deal with various constraints in the movement. The position, posture and velocity of the robot are constrained as a state of a via-point. In our algorithm, the feasible motions are planned by modifying via-points. Furthermore, we formulate the motion planning problem as a simple iterative method with a Linear Programming (LP) problem for efficiency of the motion planning. We have applied the method to generate the kicking motion of a HOAP-3 humanoid robot. We confirmed that the robot can successfully score a goal with various courses corresponding to changing conditions of the location of an obstacle. The computation time was less than two seconds. These results indicate that the proposed algorithm can achieve efficient motion planning.

Geometrical and Topological Issues in NMT-Based Modeling

1992 ◽  
Author(s):  
Mukul Saxena ◽  
Rajan Srivatsan ◽  
Jonathan E. Davis
Keyword(s):  
Data Structure ◽  
Geometric Modeling ◽  
Modeling Environment ◽  
Insertion Algorithm ◽  
The Face ◽  
Euler Operators ◽  
Application Specific ◽  
Model Topology

Abstract The Non-Manifold Topology (NMT) Radial Edge data structure, along with the supporting set of Euler operators, provides a versatile environment for modeling non-manifold domains. The operators provide the basic tools to construct and manipulate model topology. However, an implementation of the base functionality in a geometric modeling environment raises some geometry-related issues that need to be addressed to ensure the topological validity of the underlying model. This paper focuses on those issues and emphasizes the use of geometry in the implementation of topological operators. Enhancements to the topology manipulation operations are also discussed. Specifically, this paper describes (i) a geometry-based algorithm for face insertion within the Radial Edge data structure, (ii) a manifestation of the face-insertion algorithm to resolve topological ambiguities that arise in the design of topological glue operators, and (iii) enhancements to the topology deletion operators to meet application-specific requirements.

Efficient Human Motion Planning Using Recursive Dynamics and Optimal Control Techniques

1999 ◽  
Author(s):  
Janzen Lo ◽  
Dimitris Metaxas
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Closed Loop ◽  
High Efficiency ◽  
Human Motion ◽  
Lagrangian Formulation ◽  
Planning Problem ◽  
Tree Structures ◽  
Recursive Dynamics ◽  
Minimum Torque

Abstract We present an efficient optimal control based approach to simulate dynamically correct human movements. We model virtual humans as a kinematic chain consisting of serial, closed-loop, and tree-structures. To overcome the complexity limitations of the classical Lagrangian formulation and to include knowledge from biomechanical studies, we have developed a minimum-torque motion planning method. This new method is based on the use of optimal control theory within a recursive dynamics framework. Our dynamic motion planning methodology achieves high efficiency regardless of the figure topology. As opposed to a Lagrangian formulation, it obviates the need for the reformulation of the dynamic equations for different structured articulated figures. We use a quasi-Newton method based nonlinear programming technique to solve our minimum torque-based human motion planning problem. This method achieves superlinear convergence. We use the screw theoretical method to compute analytically the necessary gradient of the motion and force. This provides a better conditioned optimization computation and allows the robust and efficient implementation of our method. Cubic spline functions have been used to make the search space for an optimal solution finite. We demonstrate the efficacy of our proposed method based on a variety of human motion tasks involving open and closed loop kinematic chains. Our models are built using parameters chosen from an anthropomorphic database. The results demonstrate that our approach generates natural looking and physically correct human motions.

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.

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