Iterative relaxation of constraints: a framework for improving automated motion planning

Bayazıt, O. Burçhan; Xie, Dawen; Amato, Nancy M.

doi:10.1109/iros.2005.1545045

Cited by 37 publications

(23 citation statements)

References 24 publications

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“…Later, milestones are carried to collision-free space. In Iterative Relaxation of Constraints (IRC) method (Bayazit et al, 2005), first a relaxed version of problem is solved and then this coarse solution is used as a guide to solve original problem iteratively. The strategy of using an approximate solution to obtain a collision-free path is also used in Lazy PRM (Bohlin & Kavraki, 2001) and C-PRM (Song & Amato, 2001).…”

Section: Framework Of the Dynamically Feasible Path Planning Algorithmsmentioning

confidence: 99%

Dynamically Feasible Probabilistic Motion Planning in Complex Environments for UAVs

Koyuncu¹,

Tsourdos²

2010

Robotics 2010 Current and Future Challenges

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In this work, we consider the problem of generating practically implementable path plan for flying unmanned aerial vehicles in 3D Complex environments. This problem is complicated by the fact that, generation of the dynamically and geometrically feasible flight trajectories for agile maneuver profiles requires search of nonlinear state space of the aircraft dynamics. This work suggests a two step feasible trajectory generating approach. In the first step, the planner explores the environment through a randomized reachability tree search using an approximate line segment model. The resulting connecting path is converted into flight way points through a line-of-sight segmentation. After this first step we explain two different methods to create Dynamically Feasible Path, first one that we called Modal-Maneuver Based PRM Planner is suitable for agile unmanned aerial vehicles that their maneuvers can be define with distinct modes. This allows significant decreases in control input space and thus search dimensions, resulting in a natural way to design controllers and implement trajectory planning using the closed-form flight modes. In this approach the resulting connectivity path and the corresponding milestones are refined with a single query Probabilistic Road Map (PRM) implementation that creates dynamically feasible flight paths with distinct flight mode selections and their modal control inputs. In our second approach that we called Probabilistic B-Spline Planner, every consecutive way points are connected with B-Spline curves and these curves are repaired probabilistically to obtain a geometrically and dynamically feasible path. This generated feasible path is turned in to time depended trajectory with using time scale factor considering the velocity and acceleration limits of the aircrafts.

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Section: Framework Of the Dynamically Feasible Path Planning Algorithmsmentioning

confidence: 99%

Dynamically Feasible Probabilistic Motion Planning in Complex Environments for UAVs

Koyuncu¹,

Tsourdos²

2010

Robotics 2010 Current and Future Challenges

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“…The efficiency of these approaches decreases rapidly for chains with many links. To address this issue, researchers have developed several closure configuration generation methods that can be adapted to solve the IK problem, such as the random loop generator [18] and iterative constraint relaxation [19], which have considerably improved performance over earlier methods.…”

Section: A Prior Approachesmentioning

confidence: 99%

Inverse Kinematics for a Serial Chain with Fully Rotatable Joints

Han¹,

Rudolph²

2006

Robotics: Science and Systems II

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Abstract-Inverse kinematics (IK) problems are important in the study of robotics and have found applications in other fields such as structural biology. The conventional formulation of IK in terms of joint parameters amounts to solving a system of nonlinear equations, which is considered to be very hard for general chains, especially for those with many links.In this paper, we study IK for a serial chain with joints under distance constraints, in particular, either a spatial chain with spherical joints, or a planar chain with revolute joints (in this paper we ignore other constraints such as joint limits and link collision-free constraints, a common approach in studies of inverse kinematics). We present a new set of geometric parameters, which are not joint angles, for such chains, and use a novel approach to formulate the inverse kinematics as a system of linear inequalities, which is an exact, not an approximate, formulation of the IK problem. It follows that the IK problem for such a chain with an arbitrary number of joints can be done efficiently in many ways.Under our new formulation, the set of solutions for an IK problem (as specified by the positions of the two end points of the last link), and more generally the set of solutions for all IK problems, is essentially piecewise convex. Our approach can also be generalized to other linkages such as those with prismatic joints sandwiched between rotational joints and with multiple loops that have a tree decomposition of triangles. The efficient algorithms and nice geometry entailed by piecewise convexity considerably simplify IK related problems, including motion planning, in the systems under study, and thus broaden the class of practical mechanisms at the disposal of robot designers.

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“…Analytical approaches construct explicit geometrical and topological representation of the closure set [4], [9], [13], but are usually inefficient in practice. Practical sampling-based methods [3], [16] usually project the closure set on the subset of parameters, on which the planning is performed [5], [8]. An inverse kinematics solver is used in these approaches as a black box to get the solution back on the configuration space.…”

Section: Introductionmentioning

confidence: 99%

Motion Planning for Highly Constrained Spaces

Yershova

LaValle

2009

Robot Motion and Control 2009

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Abstract-We introduce a sampling-based motion planning method that automatically adapts to the difficulties caused by thin regions in the free space (not necessarily narrow corridors). These problems arise frequently in settings such as closed-chain manipulators, humanoid motion planning, and generally any time bodies are in contact or maintain close proximity with each other. Our method combines the aggressive exploration properties of RRTs with the intrinsic dimensionality-reduction properties of kd-trees to focus the sampling and searching in the appropriate subspaces. We handle closed-chains and other kinds of constraints in a general way that avoids inverse kinematics computations, if desired. We have implemented the method and show its computational advantages on a variety of challenging examples.

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Iterative relaxation of constraints: a framework for improving automated motion planning

Cited by 37 publications

References 24 publications

Dynamically Feasible Probabilistic Motion Planning in Complex Environments for UAVs

Dynamically Feasible Probabilistic Motion Planning in Complex Environments for UAVs

Inverse Kinematics for a Serial Chain with Fully Rotatable Joints

Motion Planning for Highly Constrained Spaces

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