Control and Motion Planning of a Nonholonomic Parallel Orienting Platform

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Janusz Jakubiak ◽  
Władyslaw Magiera ◽  
Krzysztof Tchoń
Keyword(s):  
Motion Planning ◽  
Translational Motion ◽  
Open Loop ◽  
Planning Algorithm ◽  
Parallel Platform ◽  
Practical Stabilization ◽  
Planning Problems ◽  
Form System ◽  
Loop Motion ◽  
Space Approach

An orienting platform is a mechanism which allows rotation of a spatial object without translational motion of that object. In this work, we study a parallel platform with one passive nonholonomic spherical joint and two series of spherical, actuated prismatic and universal joints (the platform is also known in literature as an (nS)-2SPU wrist). To solve the control and motion planning problems, an analytic approach is used. The design of practical stabilization and tracking algorithm is based on transverse functions and a method for motion planning respecting mechanical singularities is derived from endogenous configuration space approach. It is shown that the system is controllable and locally equivalent to the chained form system. Then, the stabilization, tracking, and motion planning algorithms are proposed. Results are verified with computer simulations. A combination of the open-loop motion planning algorithm and the closed-loop tracking provide a tool for designing a motion planning algorithm respecting mechanical singularities and robust to input disturbances.

Motion planning of the trident snake robot equipped with passive or active wheels

2012 ◽  
Vol 60 (3) ◽  
pp. 547-555 ◽  
Author(s):  
D. Paszuk ◽  
K. Tchoń ◽  
Z. Pietrowska
Keyword(s):  
Control System ◽  
Motion Planning ◽  
Computer Simulations ◽  
Configuration Space ◽  
Snake Robot ◽  
System Representation ◽  
And Control ◽  
Planning Problems ◽  
Jacobian Algorithm ◽  
Space Approach

Abstract We study the kinematics of the trident snake robot equipped with either active joints and passive wheels or passive joints and active wheels. A control system representation of the kinematics is derived, and control singularities examined. Two motion planning problems are addressed, corresponding to diverse ways of controlling the robot, and solved by means of the endogenous configuration space approach. The constraints imposed by the presence of control singularities are handled using the imbalanced Jacobian algorithm assisted by an auxiliary feedback. Performance of the motion planning algorithms is demonstrated by computer simulations.

Motion Planning for Industrial Mobile Robots With Closed-Loop Stability Enhanced Prediction

2019 ◽  
Author(s):  
Jessica Leu ◽  
Masayoshi Tomizuka
Keyword(s):  
Motion Planning ◽  
Closed Loop ◽  
Dynamic Environments ◽  
Open Loop ◽  
Human Robot Interaction ◽  
Planning Problem ◽  
Prediction Horizon ◽  
Robot Systems ◽  
Planning Algorithm ◽  
Loop Stability

Abstract Real-time, safe, and stable motion planning in co-robot systems involving dynamic human robot interaction (HRI) remains challenging due to the time varying nature of the problem. One of the biggest challenges is to guarantee closed-loop stability of the planning algorithm in dynamic environments. Typically, this can be addressed if there exists a perfect predictor that precisely predicts the future motions of the obstacles. Unfortunately, a perfect predictor is not possible to achieve. In HRI environments in this paper, human workers and other robots are the obstacles to the ego robot. We discuss necessary conditions for the closed-loop stability of a planning problem using the framework of model predictive control (MPC). It is concluded that the predictor needs to be able to detect the obstacles’ movement mode change within a time delay allowance and the MPC needs to have a sufficient prediction horizon and a proper cost function. These allow MPC to have an uncertainty tolerance for closed-loop stability, and still avoid collision when the obstacles’ movement is not within the tolerance. Also, the closed-loop performance is investigated using a notion of M-convergence, which guarantees finite local convergence (at least M steps ahead) of the open-loop trajectories toward the closed-loop trajectory. With this notion, we verify the performance of the proposed MPC with stability enhanced prediction through simulations and experiments. With the proposed method, the robot can better deal with dynamic environments and the closed-loop cost is reduced.

scholarly journals On dynamically consistent Jacobian inverse for non-holonomic robotic systems

2017 ◽  
Vol 27 (4) ◽  
pp. 555-573 ◽  
Author(s):  
Joanna Ratajczak ◽  
Krzysztof Tchoń
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Consistency Condition ◽  
Robotic Systems ◽  
Planning Problem ◽  
Commutativity Property ◽  
Kinematic Singularities ◽  
Planning Problems ◽  
Jacobian Inverse ◽  
Space Approach

AbstractThis paper presents the dynamically consistent Jacobian inverse for non-holonomic robotic system, and its application to solving the motion planning problem. The system’s kinematics are represented by a driftless control system, and defined in terms of its input-output map in accordance with the endogenous configuration space approach. The dynamically consistent Jacobian inverse (DCJI) has been introduced by means of a Riemannian metric in the endogenous configuration space, exploiting the reduced inertia matrix of the system’s dynamics. The consistency condition is formulated as the commutativity property of a diagram of maps. Singular configurations of DCJI are studied, and shown to coincide with the kinematic singularities. A parametric form of DCJI is derived, and used for solving example motion planning problems for the trident snake mobile robot. Some advantages in performance of DCJI in comparison to the Jacobian pseudoinverse are discovered.

scholarly journals MP-RRT#: a Model Predictive Sampling-based Motion Planning Algorithm for Unmanned Aircraft Systems

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
Stefano Primatesta ◽  
Abdalla Osman ◽  
Alessandro Rizzo
Keyword(s):  
Model Predictive Control ◽  
Motion Planning ◽  
Predictive Control ◽  
Unmanned Aircraft ◽  
Unmanned Aircraft Systems ◽  
Dynamic Constraints ◽  
Aircraft Systems ◽  
Planning Algorithm ◽  
Planning Problems ◽  
Optimal Graph

AbstractThis paper introduces a kinodynamic motion planning algorithm for Unmanned Aircraft Systems (UAS), called MP-RRT#. MP-RRT# joins the potentialities of RRT# with a strategy based on Model Predictive Control to efficiently solve motion planning problems under differential constraints. Similar to other RRT-based algorithms, MP-RRT# explores the map constructing an asymptotically optimal graph. In each iteration the graph is extended with a new vertex in the reference state of the UAS. Then, a forward simulation is performed using a Model Predictive Control strategy to evaluate the motion between two adjacent vertices, and a trajectory in the state space is computed. As a result, the MP-RRT# algorithm eventually generates a feasible trajectory for the UAS satisfying dynamic constraints. Simulation results obtained with a simulated drone controlled with the PX4 autopilot corroborate the validity of the MP-RRT# approach.

scholarly journals Motion Planning of a Second-Order Nonholonomic Chained Form System Based on Holonomy Extraction

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1337
Author(s):  
Masahide Ito
Keyword(s):  
Motion Planning ◽  
Nonholonomic Systems ◽  
Second Order ◽  
Literature Survey ◽  
First Order ◽  
Underactuated Manipulator ◽  
Planning Algorithm ◽  
The One ◽  
Specific Control ◽  
Form System

This paper proposes a motion planning algorithm for dynamic nonholonomic systems represented in a second-order chained form. The proposed approach focuses on the so-called holonomy resulting from a kind of motion that traverses a closed path in a reduced configuration space of the system. According to the author’s literature survey, control approaches that make explicit use of holonomy exist for kinematic nonholonomic systems but does not exist for dynamic nonholonomic systems. However, the second-order chained form system is controllable. Also, the structure of the second-order chained form system analogizes with the one of the first-order chained form for kinematic nonholonomic systems. These survey and perspectives brought a hypothesis that there exists a specific control strategy for extracting holonomy of the second-order chained form system to the author. To verify this hypothesis, this paper shows that the holonomy of the second-order chained form system can be extracted by combining two appropriate pairs of sinusoidal inputs. Then, based on such holonomy extraction, a motion planning algorithm is constructed. Furthermore, the effectiveness is demonstrated through some simulations including an application to an underactuated manipulator.

Task-priority motion planning of underactuated systems: an endogenous configuration space approach

Robotica ◽  
2009 ◽  
Vol 28 (6) ◽  
pp. 885-892 ◽  
Author(s):  
Adam Ratajczak ◽  
Joanna Karpińska ◽  
Krzysztof Tchoń
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Robotic Systems ◽  
Planning Problem ◽  
Redundant Manipulators ◽  
Container Ship ◽  
Secondary Tasks ◽  
Planning Algorithm ◽  
Task Priority ◽  
Space Approach

SUMMARYThis paper presents a task-priority motion planning algorithm for underactuated robotic systems. The motion planning algorithm combines two features: the idea of the task-priority control of redundant manipulators and the endogenous configuration space approach. This combination results in the algorithm which solves the primary motion planning task simultaneously with one or more secondary tasks ordered in accordance with decreasing priorities. The performance of the task-priority motion planning algorithm has been illustrated with computer simulations of the motion planning problem for a container ship.

scholarly journals A new method on motion planning for mobile robots using jump point search and Bezier curves

2021 ◽  
Vol 18 (4) ◽  
pp. 172988142110192
Author(s):  
Ben Zhang ◽  
Denglin Zhu
Keyword(s):  
Motion Planning ◽  
Initial Point ◽  
Target Point ◽  
Jump Point ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Front End ◽  
Planning Algorithm ◽  
Point Search ◽  
Path Planning Algorithm

Innovative applications in rapidly evolving domains such as robotic navigation and autonomous (driverless) vehicles rely on motion planning systems that meet the shortest path and obstacle avoidance requirements. This article proposes a novel path planning algorithm based on jump point search and Bezier curves. The proposed algorithm consists of two main steps. In the front end, the improved heuristic function based on distance and direction is used to reduce the cost, and the redundant turning points are trimmed. In the back end, a novel trajectory generation method based on Bezier curves and a straight line is proposed. Our experimental results indicate that the proposed algorithm provides a complete motion planning solution from the front end to the back end, which can realize an optimal trajectory from the initial point to the target point used for robot navigation.

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