scholarly journals Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems

2018 ◽  
Author(s):  
Kristoffer Bergman ◽  
Daniel Axehill
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Homotopy Methods ◽  
Planning Problems

Gradient Optimization of Inverse Dynamics for Robotic Manipulator Motion Planning Using Combined Optimal Control

2017 ◽  
Author(s):  
Shangdong Gong ◽  
Redwan Alqasemi ◽  
Rajiv Dubey
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Inverse Dynamics ◽  
Null Space ◽  
Optimal Solution ◽  
Human Motion ◽  
Optimization Techniques ◽  
Redundant Manipulators ◽  
Robot Arm ◽  
Gradient Optimization

Motion planning of redundant manipulators is an active and widely studied area of research. The inverse kinematics problem can be solved using various optimization methods within the null space to avoid joint limits, obstacle constraints, as well as minimize the velocity or maximize the manipulability measure. However, the relation between the torques of the joints and their respective positions can complicate inverse dynamics of redundant systems. It also makes it challenging to optimize cost functions, such as total torque or kinematic energy. In addition, the functional gradient optimization techniques do not achieve an optimal solution for the goal configuration. We present a study on motion planning using optimal control as a pre-process to find optimal pose at the goal position based on the external forces and gravity compensation, and generate a trajectory with optimized torques using the gradient information of the torque function. As a result, we reach an optimal trajectory that can minimize the torque and takes dynamics into consideration. We demonstrate the motion planning for a planar 3-DOF redundant robotic arm and show the results of the optimized trajectory motion. In the simulation, the torque generated by an external force on the end-effector as well as by the motion of every link is made into an integral over the squared torque norm. This technique is expected to take the torque of every joint into consideration and generate better motion that maintains the torques or kinematic energy of the arm in the safe zone. In future work, the trajectories of the redundant manipulators will be optimized to generate more natural motion as in humanoid arm motion. Similar to the human motion strategy, the robot arm is expected to be able to lift weights held by hands, the configuration of the arm is changed along from the initial configuration to a goal configuration. Furthermore, along with weighted least norm (WLN) solutions, the optimization framework will be more adaptive to the dynamic environment. In this paper, we present the development of our methodology, a simulated test and discussion of the results.

Efficient Human Motion Planning Using Recursive Dynamics and Optimal Control Techniques

1999 ◽  
Author(s):  
Janzen Lo ◽  
Dimitris Metaxas
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Closed Loop ◽  
High Efficiency ◽  
Human Motion ◽  
Lagrangian Formulation ◽  
Planning Problem ◽  
Tree Structures ◽  
Recursive Dynamics ◽  
Minimum Torque

Abstract We present an efficient optimal control based approach to simulate dynamically correct human movements. We model virtual humans as a kinematic chain consisting of serial, closed-loop, and tree-structures. To overcome the complexity limitations of the classical Lagrangian formulation and to include knowledge from biomechanical studies, we have developed a minimum-torque motion planning method. This new method is based on the use of optimal control theory within a recursive dynamics framework. Our dynamic motion planning methodology achieves high efficiency regardless of the figure topology. As opposed to a Lagrangian formulation, it obviates the need for the reformulation of the dynamic equations for different structured articulated figures. We use a quasi-Newton method based nonlinear programming technique to solve our minimum torque-based human motion planning problem. This method achieves superlinear convergence. We use the screw theoretical method to compute analytically the necessary gradient of the motion and force. This provides a better conditioned optimization computation and allows the robust and efficient implementation of our method. Cubic spline functions have been used to make the search space for an optimal solution finite. We demonstrate the efficacy of our proposed method based on a variety of human motion tasks involving open and closed loop kinematic chains. Our models are built using parameters chosen from an anthropomorphic database. The results demonstrate that our approach generates natural looking and physically correct human motions.

scholarly journals A time optimal control problem for the collision-free robot motion planning

PAMM ◽  
2011 ◽  
Vol 11 (1) ◽  
pp. 725-726
Author(s):  
Chantal Landry ◽  
Matthias Gerdts ◽  
René Henrion ◽  
Dietmar Hömberg
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Motion Planning ◽  
Control Problem ◽  
Time Optimal Control ◽  
Robot Motion ◽  
Robot Motion Planning ◽  
Time Optimal ◽  
Time Optimal Control Problem

scholarly journals Maximizing the Coverage of Roadmap Graph for Optimal Motion Planning

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-23 ◽  
Author(s):  
Jae-Han Park ◽  
Tae-Woong Yoon
Keyword(s):  
Motion Planning ◽  
Industry 4.0 ◽  
Industrial Robot ◽  
Efficient Solutions ◽  
Industrial Robots ◽  
Optimal Motion ◽  
Optimal Motion Planning ◽  
Planning Problems ◽  
Complex Planning ◽  
Satisfactory Quality

Automated motion-planning technologies for industrial robots are critical for their application to Industry 4.0. Various sampling-based methods have been studied to generate the collision-free motion of articulated industrial robots. Such sampling-based methods provide efficient solutions to complex planning problems, but their limitations hinder the attainment of optimal results. This paper considers a method to obtain the optimal results in the roadmap algorithm that is representative of the sampling-based method. We define the coverage of a graph as a performance index of its optimality as constructed by a sampling-based algorithm and propose an optimization algorithm that can maximize graph coverage in the configuration space. The proposed method was applied to the model of an industrial robot, and the results of the simulation confirm that the roadmap graph obtained by the proposed algorithm can generate results of satisfactory quality in path-finding tests under various conditions.

Tangent bundle RRT: A randomized algorithm for constrained motion planning

Robotica ◽  
2014 ◽  
Vol 34 (1) ◽  
pp. 202-225 ◽  
Author(s):  
Beobkyoon Kim ◽  
Terry Taewoong Um ◽  
Chansu Suh ◽  
F. C. Park
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Tangent Bundle ◽  
Numerical Experiments ◽  
Randomized Algorithm ◽  
Random Trees ◽  
Constrained Motion ◽  
Wide Range ◽  
Random Node ◽  
Planning Problems

SUMMARYThe Tangent Bundle Rapidly Exploring Random Tree (TB-RRT) is an algorithm for planning robot motions on curved configuration space manifolds, in which the key idea is to construct random trees not on the manifold itself, but on tangent bundle approximations to the manifold. Curvature-based methods are developed for constructing tangent bundle approximations, and procedures for random node generation and bidirectional tree extension are developed that significantly reduce the number of projections to the manifold. Extensive numerical experiments for a wide range of planning problems demonstrate the computational advantages of the TB-RRT algorithm over existing constrained path planning algorithms.

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