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.

Trajectory Planning and Obstacle Avoidance for Hyper-Redundant Serial Robots

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Midhun S. Menon ◽  
V. C. Ravi ◽  
Ashitava Ghosal
Keyword(s):  
Motion Planning ◽  
Obstacle Avoidance ◽  
Medical Robotics ◽  
Theoretical Development ◽  
Wheeled Mobile Robots ◽  
Calculus Of Variation ◽  
Redundant Robot ◽  
Cluttered Environments ◽  
Serial Robots ◽  
Actuated Joints

Hyper-redundant snakelike serial robots are of great interest due to their application in search and rescue during disaster relief in highly cluttered environments and recently in the field of medical robotics. A key feature of these robots is the presence of a large number of redundant actuated joints and the associated well-known challenge of motion planning. This problem is even more acute in the presence of obstacles. Obstacle avoidance for point bodies, nonredundant serial robots with a few links and joints, and wheeled mobile robots has been extensively studied, and several mature implementations are available. However, obstacle avoidance for hyper-redundant snakelike robots and other extended articulated bodies is less studied and is still evolving. This paper presents a novel optimization algorithm, derived using calculus of variation, for the motion planning of a hyper-redundant robot where the motion of one end (head) is an arbitrary desired path. The algorithm computes the motion of all the joints in the hyper-redundant robot in a way such that all its links avoid all obstacles present in the environment. The algorithm is purely geometric in nature, and it is shown that the motion in free space and in the vicinity of obstacles appears to be more natural. The paper presents the general theoretical development and numerical simulations results. It also presents validating results from experiments with a 12-degree-of-freedom (DOF) planar hyper-redundant robot moving in a known obstacle field.

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.

On Second Order Efficiency of Minimum Discrepancy and Minimum Distance Estimators for the Multinomial Distribution

1988 ◽  
Vol 37 (1-2) ◽  
pp. 17-28 ◽  
Author(s):  
B. N. Nagnur ◽  
M.S. Hegde
Keyword(s):  
Minimum Distance ◽  
Multinomial Distribution ◽  
Second Order ◽  
Distance Functions ◽  
Asymptotically Normal ◽  
Minimum Discrepancy ◽  
Second Order Efficiency ◽  
Minimum Distance Estimators ◽  
Power Divergence ◽  
Asymptotically Efficient

Rao (1961, '62, '63) introduced the concept of second order efficiency (s.o.e.) of an asymptotically efficient i.e., best asymptotically normal (BAN) estimator. The main purpose of introducing this concept was to discriminate different asymptotically efficient estimators. Rao considered some wellknown methods of estimation for the multinomial distribution with true cell probabilities depending on a single unknown parameter. Nagnur and Aithal (1986) obtained a general expression for the s.o.e. of minimum distance estimators, obtained from a particular form of a distance function given by Taylor (1953) for the multinomial distribution . In this paper we have obtained the expression for the s.o.e. of minimum discrepancy (minimum power-divergence) estimators, obtained from a discrepancy function defined by Cressie and Read (1984) . The distance functions and the discrepancy functions which produce estimators having the same s.o.e. have been identified.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

scholarly journals Higher-order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties

2021 ◽  
Vol 22 (2) ◽  
pp. 1-37
Author(s):  
Christopher H. Broadbent ◽  
Arnaud Carayol ◽  
C.-H. Luke Ong ◽  
Olivier Serre
Keyword(s):  
Model Checking ◽  
Free Variable ◽  
Higher Order ◽  
Second Order ◽  
Effective Solution ◽  
Parity Games ◽  
Transition Graphs ◽  
Second Order Logic ◽  
Pushdown Automata ◽  
Monadic Second Order Logic

This article studies the logical properties of a very general class of infinite ranked trees, namely, those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal -calculus, three main problems: model-checking, logical reflection (a.k.a. global model-checking, that asks for a finite description of the set of elements for which a formula holds), and selection (that asks, if exists, for some finite description of a set of elements for which an MSO formula with a second-order free variable holds). For each of these problems, we provide an effective solution. This is obtained, thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible pushdown automata.

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