Optimized-Motion Planning: Theory and Implementation
The first handbook to the practical specifics of motion planning, Optimized-Motion Planning offers design engineers methods and insights for solving real motion planning problems in a 3-dimensional space. Complete with a disk of software programs, this unique guide allows users to design, test, and implement possible solutions, useful in a host of contexts, especially tool path planning. Beginning with a brief overview of the general class of problems examined within the book as well as available solution techniques, Part 1 familiarizes the reader with the conceptual threads that underlie each approach. This early discussion also considers the specific applications of each technique as well as its computational efficiency. Part 2 illustrates basic problem-solving methodology by considering the case of a point moving between stationary polygons in a plane. This section features algorithms for data organization and storage, the concepts of passage networks and feasibility charts, as well as the path optimization algorithm. Elaborating on the problematic model described in Part 2, Part 3 develops an algorithm for optimizing the motion of a point between stationary polyhedra in a 3-dimensional space. This algorithm is first applied to the case of nonpoint objects moving between obstacles that can be stationary or moving with known patterns. It's then used in connection with the extensively investigated problem of motion planning for multilink manipulators.
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2-gate slice 3-dimensional space adjacent algorithm backtracking C-space obstacles cells Chapter collision-free path connection-face constraints continuity-segments convex convex polygonal coordinates curnode cylindrical algebraic decomposition decomposition delete described disk end point entry example considered expanded obstacle extending chain face feasibility chart feasible path free space given goal positions Hence hypercube Input intersection jump-node last node Major Drawbacks manipulator method minimum allowable clearance motion motion-planning moving object negative x-direction node reached node representing number of edges operation optimized path orientation partially constructed passage partially constructed path passage network piecewise linear plane chain plane graph point moving polygonal obstacles polyhedral obstacles polytope primary vertex problem red-black tree reference point Robotics rotation safe configurations secondary vertices semialgebraic set set of safe shortest path shown in Figure Silicon Graphics Step straight-line segment subpath-generation function tangency-segments target object total number trajectory unfolded vectors velocities and accelerations vertex of contact visibility-slice y-coordinate