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.

Optimal Control and Path Planning of a 3PRS Robot Using Indirect Variation Algorithm

Robotica ◽  
2019 ◽  
Vol 38 (5) ◽  
pp. 903-924 ◽  
Author(s):  
H. Tourajizadeh ◽  
O. Gholami
Keyword(s):  
Optimal Control ◽  
Lagrange Multipliers ◽  
Inverse Dynamics ◽  
Null Space ◽  
Load Capacity ◽  
Optimal Path ◽  
Maximum Load ◽  
Optimization Method ◽  
Matlab Simulation ◽  
Prismatic Joints

SUMMARYIn this paper, optimal control of a 3PRS robot is performed, and its related optimal path is extracted accordingly. This robot is a kind of parallel spatial robot with six DOFs which can be controlled using three active prismatic joints and three passive rotary ones. Carrying a load between two initial and final positions is the main application of this robot. Therefore, extracting the optimal path is a valuable study for maximizing the load capacity of the robot. First of all, the complete kinematic and kinetic modeling of the robot is extracted to control and optimize the robot. As the robot is categorized as a constrained robot, its kinematics is studied using a Jacobian matrix and its pseudo inverse whereas its kinetics is studied using Lagrange multipliers. The robot is then controlled using feedforward term of the inverse dynamics. Afterward, the extracted dynamics equation of the robot is transferred to state space to be employed for calculus of variations. Considering the constrained entity of the robot, null space of the robot is employed to eliminate the Lagrange multipliers to provide the applicability of indirect variation algorithm for the robot. As a result, not only are the optimal controlling signals calculated but also the corresponding optimal path of the robot between two boundary conditions is extracted. All the modeling, controlling, and optimization process are verified using MATLAB simulation. The profiles are then double-checked by comparing the results with SimMechanics. It is proved that with the aid of the proposed controlling and optimization method of this article, the robot can be controlled along its optimal path through which the maximum load can be carried.

Inverse Dynamics of a Flexible Robot Arm by Optimal Control

1993 ◽  
Vol 115 (2) ◽  
pp. 289-293 ◽  
Author(s):  
T. Kokkinis ◽  
M. Sahraian
Keyword(s):  
Optimal Control ◽  
Inverse Dynamics ◽  
Robot Arm ◽  
Flexible Robot ◽  
Joint Torques ◽  
Practical Applications ◽  
End Point ◽  
Point Tracking ◽  
Flexible Arms ◽  
High Frequency Content

The problem of end-point positioning of flexible arms is discussed. Because of the nonminimum phase nature of the problem, inversion fails to produce bounded joint torques. Bounded noncausal joint torques for achieving the task of end-point tracking for a multilink arm are found using optimal control theory. The torques obtained have no high-frequency content, and are suitable for practical applications. The method is illustrated by simulation of a single-link arm, for which stability and robustness considerations for design are given.

scholarly journals Enhancing Digital Human Motion Planning of Assembly Tasks Through Dynamics and Optimal Control

Procedia CIRP ◽  
2016 ◽  
Vol 44 ◽  
pp. 20-25 ◽  
Author(s):  
Staffan Björkenstam ◽  
Niclas Delfs ◽  
Johan S. Carlson ◽  
Robert Bohlin ◽  
Bengt Lennartson
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Human Motion ◽  
Digital Human ◽  
Assembly Tasks

Inverse Dynamics for Discrete Geometric Mechanics of Multibody Systems With Application to Direct Optimal Control

2018 ◽  
Vol 13 (10) ◽  
Author(s):  
Staffan Björkenstam ◽  
Sigrid Leyendecker ◽  
Joachim Linn ◽  
Johan S. Carlson ◽  
Bengt Lennartson
Keyword(s):  
Optimal Control ◽  
Multibody Systems ◽  
Inverse Dynamics ◽  
Broad Class ◽  
Equations Of Motion ◽  
Human Motion ◽  
Planning Problem ◽  
Unit Quaternions ◽  
Rigid Multibody Systems ◽  
Digital Human

In this paper, we present efficient algorithms for computation of the residual of the constrained discrete Euler–Lagrange (DEL) equations of motion for tree structured, rigid multibody systems. In particular, we present new recursive formulas for computing partial derivatives of the kinetic energy. This enables us to solve the inverse dynamics problem of the discrete system with linear computational complexity. The resulting algorithms are easy to implement and can naturally be applied to a very broad class of multibody systems by imposing constraints on the coordinates by means of Lagrange multipliers. A comparison is made with an existing software package, which shows a drastic improvement in computational efficiency. Our interest in inverse dynamics is primarily to apply direct transcription optimal control methods to multibody systems. As an example application, we present a digital human motion planning problem, which we solve using the proposed method. Furthermore, we present detailed descriptions of several common joints, in particular singularity-free models of the spherical joint and the rigid body joint, using the Lie groups of unit quaternions and unit dual quaternions, respectively.

scholarly journals Motion Planning and Control of Redundant Manipulators for Dynamical Obstacle Avoidance

2021 ◽  
Author(s):  
Giacomo Palmieri ◽  
Cecilia Scoccia ◽  
Matteo-Claudio Palpacelli ◽  
Massimo Callegari
Keyword(s):  
Path Planning ◽  
Motion Planning ◽  
Motion Control ◽  
Null Space ◽  
Computational Effort ◽  
Control Law ◽  
Redundant Manipulators ◽  
Planning And Control ◽  
On Line ◽  
And Control

This paper presents a framework for the motion planning and control of redundant manipulators with the added task of collision avoidance. The algorithms that were previously studied and tested by the authors for planar cases are here extended to full mobility redundant manipulators operating in a three-dimensional workspace. The control strategy consists of a combination of off-line path planning algorithms with on-line motion control. The path planning algorithm is used to generate trajectories able to avoid fixed obstacles, detected before the robot starts to move; it is based on the potential fields method combined with a smoothing interpolation that exploits Bézier curves. The on-line motion control is designed to compensate for the motion of the obstacles and to avoid collisions along the kinematic chain of the manipulator; it is realized by means of a velocity control law based on the null space method for redundancy control. A term of the control law takes into account the speed of the obstacles as well as their position. In order to test the algorithms, a set of simulations are presented: the robot KUKA LBR iiwa is controlled in different cases, where fixed or dynamic obstacles interfere with its motion. Simulations are also used to estimate the required computational effort in order to verify the transferability to a real system.

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