Motion planning

About: Motion planning is a research topic. Over the lifetime, 32846 publications have been published within this topic receiving 553548 citations.

Diffusion-Based Motion Planning for a Nonholonomic Flexible Needle Model

Abstract: Fine needles facilitate diagnosis and therapy because they enable minimally invasive surgical interventions. This paper formulates the problem of steering a very flexible needle through firm tissue as a nonholonomic kinematics problem, and demonstrates how planning can be accomplished using diffusion-based motion planning on the Euclidean group, SE(3). In the present formulation, the tissue is treated as isotropic and no obstacles are present. The bevel tip of the needle is treated as a nonholonomic constraint that can be viewed as a 3D extension of the standard kinematic cart or unicycle. A deterministic model is used as the starting point, and reachability criteria are established. A stochastic differential equation and its corresponding Fokker-Planck equation are derived. The Euler-Maruyama method is used to generate the ensemble of reachable states of the needle tip. Inverse kinematics methods developed previously for hyper-redundant and binary manipulators that use this probability density information are applied to generate needle tip paths that reach the desired targets.

Path Planning Based on Bézier Curve for Autonomous Ground Vehicles

Abstract: In this paper we present two path planning algorithms based on Bezier curves for autonomous vehicles with way points and corridor constraints. Bezier curves have useful properties for the path generation problem. The paper describes how the algorithms apply these properties to generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segments smoothly to generate the path. Additionally, we discuss the constrained optimization problem that optimizes the resulting path for a user-defined cost function. The simulation shows the generation of successful routes for autonomous vehicles using these algorithms as well as control results for a simple kinematic vehicle. Extensions of these algorithms towards navigating through an unstructured environment with limited sensor range are discussed.

Shortest path synthesis for Dubins non-holonomic robot

Abstract: We calculate the partition of the configuration space R/sup 2//spl times/S/sup 1/ of a car-like robot, only moving forwards, with respect to the type of the length optimal paths. This kind of robot is subject to kinematic constraints on its path curvature and its orientation. Starting from the results on shortest paths, we give new optimality conditions on these paths, and compute the partition for any horizontal plane of the configuration space. >

Circumventing dynamic modeling: evaluation of the error-state Kalman filter applied to mobile robot localization

Abstract: The mobile robot localization problem is treated as a two-stage iterative estimation process. The attitude is estimated first and is then available for position estimation. The indirect (error state) form of the Kalman filter is developed for attitude estimation when applying gyro modeling. The main benefit of this choice is that combined dynamic modeling of the mobile robot and its interaction with the environment is avoided. The filter optimally combines the attitude rate information from the gyro and the absolute orientation measurements. The proposed implementation is independent of the structure of the vehicle or the morphology of the ground. The method can easily be transferred to another mobile platform provided it carries an equivalent set of sensors. The 2D case is studied in detail first. Results of extending the approach to the 3D case are presented. In both cases the results demonstrate the efficacy of the proposed method.

Robust online motion planning via contraction theory and convex optimization

Abstract: We present a framework for online generation of robust motion plans for robotic systems with nonlinear dynamics subject to bounded disturbances, control constraints, and online state constraints such as obstacles. In an offline phase, one computes the structure of a feedback controller that can be efficiently implemented online to track any feasible nominal trajectory. The offline phase leverages contraction theory and convex optimization to characterize a fixed-size “tube” that the state is guaranteed to remain within while tracking a nominal trajectory (representing the center of the tube). In the online phase, when the robot is faced with obstacles, a motion planner uses such a tube as a robustness margin for collision checking, yielding nominal trajectories that can be safely executed, i.e., tracked without collisions under disturbances. In contrast to recent work on robust online planning using funnel libraries, our approach is not restricted to a fixed library of maneuvers computed offline and is thus particularly well-suited to applications such as UAV flight in densely cluttered environments where complex maneuvers may be required to reach a goal. We demonstrate our approach through simulations of a 6-state planar quadrotor navigating cluttered environments in the presence of a cross-wind. We also discuss applications of our approach to Tube Model Predictive Control (TMPC) and compare the merits of our method with state-of-the-art nonlinear TMPC techniques.