Completeness of Randomized Kinodynamic Planners with State-based Steering

Probabilistic completeness is an important property in motion planning. Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems. In this paper, we focus on an important class of kinodynamic planners, namely those that interpolate trajectories in the state space. We provide a proof of probabilistic completeness for these planners under assumptions that can be readily verified from the system's equations of motion and the user-defined interpolation function. Our proof relies crucially on a property of interpolated trajectories, termed second-order continuity (SOC), which we show is tightly related to the ability of a planner to benefit from denser sampling. We analyze the impact of this property in simulations on a low-torque pendulum. Our results show that a simple RRT using a second-order continuous interpolation swiftly finds solution, while it is impossible for the same planner using standard Bezier curves (which are not SOC) to find any solution.Comment: 21 pages, 5 figure

Automatic motion of manipulator using sampling based motion planning algorithms - application in service robotics

The thesis presents new approaches for autonomous motion execution of a robotic arm. The calculation of the motion is called motion planning and requires the computation of robot arm's path. The text covers the calculation of the path and several algorithms have been therefore implemented and tested in several real scenarios. The work focuses on sampling based planners, which means that the path is created by connecting explicitly random generated points in the free space. The algorithms can be divided into three categories: those that are working in configuration space(C-Space)(C- Space is the set of all possible joint angles of a robotic arm) , the mixed approaches using both Cartesian and C-Space and those that are using only the Cartesian space. Although Cartesian space seems more appropriate, due to dimensionality, this work illustrates that the C-Space planners can achieve comparable or better results. Initially an enhanced approach for efficient collision detection in C-Space, used by the planners, is presented. Afterwards the N dimensional cuboid region, notated as Rq, is defined. The Rq configures the C-Space so that the sampling is done close to a selected, called center, cell. The approach is enhanced by the decomposition of the Cartesian space into cells. A cell is selected appropriately if: (a) is closer to the target position and (b) lies inside the constraints. Inverse kinematics(IK) are applied to calculate a centre configuration used later by the Rq. The CellBiRRT is proposed and combines all the features. Continuously mixed approaches that do not require goal configuration or an analytic solution of IK are presented. Rq regions as well as Cells are also integrated in these approaches. A Cartesian sampling based planner using quaternions for linear interpolation is also proposed and tested. The common feature of the so far algorithms is the feasibility which is normally against the optimality. Therefore an additional part of this work deals with the optimality of the path. An enhanced approach of CellBiRRT, called CellBiRRT*, is developed and promises to compute shorter paths in a reasonable time. An on-line method using both CellBiRRT and CellBiRRT* is proposed where the path of the robot arm is improved and recalculated even if sudden changes in the environment are detected. Benchmarking with the state of the art algorithms show the good performance of the proposed approaches. The good performance makes the algorithms suitable for real time applications. In this work several applications are described: Manipulative skills, an approach for an semi-autonomous control of the robot arm and a motion planning library. The motion planning library provides the necessary interface for easy use and further development of the motion planning algorithms. It can be used as the part connecting the manipulative skill designing and the motion of a robotic arm