We prove that it is NP-hard to decide whether two points in a polygonal domain with holes can be connected by a wire. This implies that finding any approximation to the shortest path for a long snake amidst polygonal obstacles is NP-hard. On the positive side, we show that snake's problem is "length-tractable": if the snake is "fat", i.e., its length width ratio is small, the shortest path can be computed in polynomial time.
Motion planning for an object with few degrees of freedom may be approached with the cell decomposition techniques @cite_12 @cite_9 . Closest to our bounded-length snake problem is the work on path planning for a segment (rod) @cite_21 @cite_13 @cite_18 @cite_4 . Short snakes are also relevant to more recent applications of motor protein motion @cite_10 @cite_7 .
@cite_18 @cite_4 @cite_7 @cite_10 @cite_9 @cite_21 @cite_13 @cite_12
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In this paper we consider the motion planning problem of humanoid with articulated-spine for object manipulation in double support phase. Complexity of motion planning increases due to higher degrees-of-freedom (DOF), redundancy arising due to articulated spine, inherent underactuation and stability constraint. Additionally, loop-closure constraints arise during double-support phase, and self-collision constraints exist independent of the task to be performed. These problems make motion planning of humanoids a challenging task. In this work, we address the above issues by proposing a sampling based approach for planning the motion of the humanoid. Our approach to the problem is based on RRT* which can generate asymptotically optimal paths. The proposed approach deals with the stability constraints by rejective sampling approach which divides random configurations generated into valid and invalid configurations. Additionally, the loop-closure constraints are tackled by separating the humanoid into two open-kinematic sub-chains, and then generating random configurations in one sub-chain whereas the remaining sub-chain uses inverse kinematics for closure. Efficacy of the proposed approach is demonstrated for whole-body motion planning of a 25-DOF humanoid in generating asymptotically optimal end-effector paths. Abstract Time-optimal motion planning is one of the most essential problems in robotic theories. The presented direct transcription approach uses convex optimisation method to obtain a minimum-time control for robot manipulators. One subset of motion planning is the waiter motion problem that consists of moving a tablet from one place to another as fast as possible, avoiding the slip of the object that is placed upon it. In this paper the direct transcription method is presented in order to solve the waiter problem. This path tracking problem is also approximated by sequential two dimensional second-order cone programs (SOCP) using nonlinear change of variables. The computational benefit of the sequential method compared to the direct transcription approach is presented. The waiter motion problem is validated by real-life experimental results with a 6-DoF robotic arm. In this paper, we describe a strategy for integrated task and motion planning based on performing a symbolic search for a sequence of high-level operations, such as pick, move and place, while postponing geometric decisions. Partial plans (skeletons) in this search thus pose a geometric constraintsatisfaction problem (CSP), involving sequences of placements and paths for the robot, and grasps and locations of objects. We propose a formulation for these problems in a discretized configuration space for the robot. The resulting problems can be solved using existing methods for discrete CSP. Considers the problem of robot motion planning using an approximate cell decomposition method for Cspace representation. By means of a hierarchical multilevel discretization the authors are able to reduce the complexity of the problem and to provide a practically feasible procedure for its solution. Hierarchical discretization is based on the use of a multisource distance field that is introduced and described in the paper. The developed procedure, used as an heuristic, systematically reduces the amount of memory needed for implementing the motion planning algorithm. Using such a procedure, several instances of the motion planning problem, involving for example two three-links manipulators acting in the same tridimensional environment, have been solved in a reasonable amount of time. >