Motion Planning for a Spherical Mobile Robot: Revisiting the Classical Ball-Plate Problem

2002 ◽  
Vol 124 (4) ◽  
pp. 502-511 ◽  
Author(s):  
Ranjan Mukherjee ◽  
Mark A. Minor ◽  
Jay T. Pukrushpan
Keyword(s):  
Motion Planning ◽  
Kinematic Model ◽  
Parallel Transport ◽  
Planning Problem ◽  
Stabilizing Controller ◽  
Line Segments ◽  
Planning And Control ◽  
Hazardous Environments ◽  
Straight Line ◽  
Spherical Mobile Robot

In comparison to wheeled robots, spherical mobile robots offer greater mobility, stability, and scope for operation in hazardous environments. Inspite of these advantages, spherical designs have failed to gain popularity due to complexity of their motion planning and control problems. In this paper, we address the motion planning problem for the rolling sphere, often referred in the literature as the “ball-plate problem,” and propose two different algorithms for reconfiguration. The first algorithm, based on simple geometry, uses a standard kinematic model and invokes alternating inputs to obtain a solution comprised of circular arcs and straight line segments. The second algorithm is based on the Gauss-Bonet theorem of parallel transport and achieves reconfiguration through spherical triangle maneuvers. While the second algorithm is inherently simple and provides a solution comprised of straight line segments only, the first algorithm provides the basis for development of a stabilizing controller. Our stabilizing controller, which will be presented in our next paper, will be the first solution to a problem that has eluded many researchers since the kinematic model of the sphere cannot be converted to chained form. Both our algorithms require numerical computation of a small number of parameters and provide the scope for easy implementation.

IMPLICIT POINT LOCATION IN ARRANGEMENTS OF LINE SEGMENTS, WITH AN APPLICATION TO MOTION PLANNING

1994 ◽  
Vol 04 (04) ◽  
pp. 369-383
Author(s):  
PANKAJ K. AGARWAL ◽  
MARC VAN KREVELD
Keyword(s):  
Data Structure ◽  
Motion Planning ◽  
Location Problem ◽  
Translational Motion ◽  
Planning Problem ◽  
Final Position ◽  
Point Location ◽  
Line Segments ◽  
Planar Region ◽  
The Face

Let [Formula: see text] be a set of n (possibly intersecting) line segments in the plane. We show that the arrangement of [Formula: see text] can be stored implicitly in a data structure of size O(n log 2n) so that the following query can be answered in time O(n1/2 log 2 n): Given two query points, determine whether they lie in the same face of the arrangement of S and, if so, return a path between them that lies within the face. This version of the implicit point location problem is motivated by the following motion planning problem: Given a polygonal robot R with m vertices and a planar region bounded by polygonal obstacles with n vertices in total, preprocess them into a data structure so that, given initial and final positions of R, one can quickly determine whether there exists a continuous collision-free translational motion of R from the initial to the final position. We show that such a query can be answered in time O((mn)1/2 log 2 mn) using O(mn log 2 mn) storage.

scholarly journals Ship Motion Planning for MASS Based on a Multi-Objective Optimization HA* Algorithm in Complex Navigation Conditions

2021 ◽  
Vol 9 (10) ◽  
pp. 1126
Author(s):  
Meiyi Wu ◽  
Anmin Zhang ◽  
Miao Gao ◽  
Jiali Zhang
Keyword(s):  
Motion Planning ◽  
Autonomous Navigation ◽  
Optimal Path ◽  
Kinematic Model ◽  
Ship Motion ◽  
Planning Problem ◽  
Navigation Systems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Three Degree Of Freedom

Ship motion planning constitutes the most critical part in the autonomous navigation systems of marine autonomous surface ships (MASS). Weather and ocean conditions can significantly affect their navigation, but there are relatively few studies on the influence of wind and current on motion planning. This study investigates the motion planning problem for USV, wherein the goal is to obtain an optimal path under the interference of the navigation environment (wind and current), and control the USV in order to avoid obstacles and arrive at its destination without collision. In this process, the influences of search efficiency, navigation safety and energy consumption on motion planning are taken into consideration. Firstly, the navigation environment is constructed by integrating information, including the electronic navigational chart, wind and current field. Based on the environmental interference factors, the three-degree-of-freedom kinematic model of USVs is created, and the multi-objective optimization and complex constraints are reasonably expressed to establish the corresponding optimization model. A multi-objective optimization algorithm based on HA* is proposed after considering the constraints of motion and dynamic and optimization objectives. Simulation verifies the effectiveness of the algorithm, where an efficient, safe and economical path is obtained and is more in line with the needs of practical application.

Kinematic Control of Nonholonomic Wheeled Mobile Manipulator: A Differential Flatness Approach

2008 ◽  
Author(s):  
Chin Pei Tang ◽  
Patrick T. Miller ◽  
Venkat N. Krovi ◽  
Ji-Chul Ryu ◽  
Sunil K. Agrawal
Keyword(s):  
Motion Planning ◽  
Kinematic Model ◽  
Pole Placement ◽  
Mobile Manipulator ◽  
Differential Flatness ◽  
Placement Problem ◽  
Planning And Control ◽  
Polynomial Curve ◽  
Point Motion ◽  
Point To Point

This paper presents an integrated motion planning and control framework for a nonholonomic wheeled mobile manipulator (WMM) system taking advantage of the (differential) flatness property. We first develop the kinematic model of the system and analyze its flatness properties. Subsequently, a statically feedback linearizable system description is developed by appropriately choosing the flat outputs. Motion-planning can now be achieved by polynomial curve fitting to satisfying the terminal conditions in the flat output space while control design reduces to a pole-placement problem for a linear system. A case study of point-to-point motion is considered to study the effectiveness of pose stabilization in the WMM. The simulation and experimental results highlight the ease-of-implementation of proposed method for online real-time integrated motion-planning/control within a hardware-in-the-loop (HIL) electro-mechanical testing.

scholarly journals Aplicación de Muestreo basado en Modelos de Control Predictivo a un Vehículo Autónomo Subacuático

2010 ◽  
Vol 4 (7) ◽  
pp. 55
Author(s):  
Charmane V. Caldwell ◽  
Damion D. Dunlap ◽  
Emmanuel G. Collins
Keyword(s):  
Model Predictive Control ◽  
Motion Planning ◽  
Predictive Control ◽  
Planning Process ◽  
Autonomous Underwater Vehicle ◽  
Kinematic Model ◽  
Local Minima ◽  
Cluttered Environments ◽  
Unmanned Underwater Vehicles ◽  
Planning And Control

Unmanned Underwater Vehicles (UUVs) can be utilized to perform difficult tasks in cluttered environments such as harbor and port protection. However, since UUVs have nonlinear and highly coupled dynamics, motion planning and control can be difficult when completing complex tasks. Introducing models into the motion planning process can produce paths the vehicle can feasibly traverse. As a result, Sampling-Based Model Predictive Control (SBMPC) is proposed to simultaneously generate control inputs and system trajectories for an autonomous underwater vehicle (AUV). The algorithm combines the benefits of sampling-based motion planning with model predictive control (MPC) while avoiding some of the major pitfalls facing both traditional sampling-based planning algorithms and traditional MPC. The method is based on sampling (i.e., discretizing) the input space at each sample period and implementing a goal-directed optimization (e.g., A*) in place of standard numerical optimization. This formulation of MPC readily applies to nonlinear systems and avoids the local minima which can cause a vehicle to become immobilized behind obstacles. The SBMPC algorithm is applied to an AUV in a 2D cluttered environment and an AUV in a common local minima problem. The algorithm is then used on a full kinematic model to demonstrate the benefits.

Kinematics, kinematic constraints and path planning for wheeled mobile robots

Robotica ◽  
1994 ◽  
Vol 12 (5) ◽  
pp. 391-400 ◽  
Author(s):  
Yongji Wang ◽  
J.A. Linnett ◽  
J. Roberts
Keyword(s):  
Path Planning ◽  
Nonholonomic Constraint ◽  
Kinematic Model ◽  
Constraint Equation ◽  
Analytic Solutions ◽  
Planning Problem ◽  
General Description ◽  
Wheeled Mobile Robots ◽  
Straight Line ◽  
Path Planning Problem

SUMMARYThe problem associated with planning a collision-free path for a wheeled mobile robot (WMR) moving among obstacles in the workspace is investigated in this paper. A kinematic model, including the general nonholonomic constraint equation, is developed first, followed by the analysis of some general maneuvering characteristics of the WMR. The analytic solutions to the typical path curves, such as circle and straight line, which are important in the path planning problem, are also derived. From the analysis of the established kinematic model, some factors which affect the path planning problem for a WMR and therefore must be taken into account are revealed and the general description of the path planning problem for a WMR is formuated. In conclusion, a possible architecture of the algorithm for a practical WMR is presented.

Planning Tendon Paths Using an Interactive Graphic Workstation

1990 ◽  
Vol 112 (4) ◽  
pp. 387-391 ◽  
Author(s):  
Inmo Yoon ◽  
D. E. Thompson
Keyword(s):  
Tendon Transfer ◽  
Kinematic Model ◽  
Ct Scans ◽  
Display System ◽  
Thumb Reconstruction ◽  
Line Segments ◽  
Reconstruction Surgery ◽  
Planar Curve ◽  
Straight Line ◽  
Log File

This study provides a technique to be used for planning tendon paths in thumb reconstruction surgery. All mathematical modeling computations are performed on a VAX 11/750 host computer and the graphic manipulation is carried out by the Evans & Sutherland PS390 color display system. The results of the simulation are stored in a log file, including the rotation angles of the joints and the location of the pulley and the insertion points as a record of the tendon transfer design for a specific hand. The methods are based on the modeling of two separate types of tendon paths that consist of straight line segments and curved segments that follow bone contours. The method further assumes that the path of the tendon will always evolve to a planar curve. By integrating this technique with an existing kinematic model of the hand derived from CT-scans, a clinically relevant method has been developed.

scholarly journals A solution to the motion planning and control problem of a car-like robot via a single-layer perceptron

Robotica ◽  
2013 ◽  
Vol 32 (6) ◽  
pp. 935-952 ◽  
Author(s):  
Avinesh Prasad ◽  
Bibhya Sharma ◽  
Jito Vanualailai
Keyword(s):  
Motion Planning ◽  
Direct Method ◽  
A Priori ◽  
Kinematic Model ◽  
Single Layer ◽  
Target Position ◽  
Homogeneous System ◽  
Planning And Control ◽  
And Control ◽  
Posture Stability

SUMMARYThis paper tackles the problem of motion planning and control of a car-like robot in an obstacle-ridden workspace. A kinematic model of the vehicle, governed by a homogeneous system of first-order differential equations, is used. A solution to the multi-tasking problem of target convergence, obstacle avoidance, and posture control is then proposed. The approach of solving the problem is two-fold. Firstly, a novel velocity algorithm is proposed to drive the car-like robot from its initial position to the target position. Secondly, a single layer artificial neural network is trained to avoid disc-shaped obstacles and provide corresponding weights, which are then used to develop a function for the steering angles. Thus, our method does not need a priori knowledge of the environment except for the goal position. With the help of the Direct Method of Lyapunov, it is shown that the proposed forms of the velocity and steering angle ensure point stability. For posture stability, we model the two parallel boundaries of a row-structured parking bay as continua of disk-shaped obstacles. Thus, our method is extendable to ensuring posture stability, which gives the desired final orientation. Computer simulations of the generated path are presented to illustrate the effectiveness of the method.

scholarly journals Improved hybrid A* path planning method for spherical mobile robot based on pendulum

2021 ◽  
Vol 18 (1) ◽  
pp. 172988142199295
Author(s):  
Ziang Zhang ◽  
Yixu Wan ◽  
You Wang ◽  
Xiaoqing Guan ◽  
Wei Ren ◽  
...  
Keyword(s):  
Mobile Robots ◽  
Common Ground ◽  
Kinematic Model ◽  
Point Contact ◽  
Shell Shape ◽  
Spherical Robot ◽  
Trajectory Tracking Control ◽  
Novel Method ◽  
Turning Radius ◽  
Spherical Mobile Robot

This article proposes a modification of hybrid A* method used for navigation of spherical mobile robots with the ability of limited partial lateral movement driven by pendulum. For pendulum-driven spherical robots with nonzero minimal turning radius, our modification helps to find a feasible and achievable path, which can be followed in line with the low time cost. Because of spherical shell shape, the robot is point contact with the ground, showing different kinematic model compared with common ground mobile robots such as differential robot and wheeled car-like robot. Therefore, this article analyzes the kinematic model of spherical robot and proposes a novel method to generate feasible and achievable paths conforming to kinematic constraints, which can be the initial value of future trajectory tracking control and further optimization. A concept of optimal robot’s minimum area for rotation is also proposed to improve search efficiency and ensure the ability of turning to any orientation by moving forward and backward in a finite number of times within limited areas.

scholarly journals Normal form approach in the motion planning of space robots: a case study

2021 ◽  
Author(s):  
Krzysztof Tchoń ◽  
Katarzyna Zadarnowska
Keyword(s):  
Normal Form ◽  
Motion Planning ◽  
Normal Forms ◽  
Inverse Dynamics ◽  
Planning Problem ◽  
Inverse Dynamics Problem ◽  
Velocity Level ◽  
Form Approach ◽  
Space Approach

AbstractWe examine applicability of normal forms of non-holonomic robotic systems to the problem of motion planning. A case study is analyzed of a planar, free-floating space robot consisting of a mobile base equipped with an on-board manipulator. It is assumed that during the robot’s motion its conserved angular momentum is zero. The motion planning problem is first solved at velocity level, and then torques at the joints are found as a solution of an inverse dynamics problem. A novelty of this paper lies in using the chained normal form of the robot’s dynamics and corresponding feedback transformations for motion planning at the velocity level. Two basic cases are studied, depending on the position of mounting point of the on-board manipulator. Comprehensive computational results are presented, and compared with the results provided by the Endogenous Configuration Space Approach. Advantages and limitations of applying normal forms for robot motion planning are discussed.

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