A PROJECTED GRADIENT AUGMENTED LAGRANGIAN APPROACH TO MULTI-OBJECTIVE TRAJECTORY PLANNING OF REDUNDANT ROBOTS

2007 ◽  
Vol 31 (4) ◽  
pp. 391-405 ◽  
Author(s):  
Amar KHOUKHI ◽  
Luc BARON ◽  
Marek BALAZINSKI

In this paper, a multi-objective trajectory planning system is developed for redundant manipulators. This system involves kinematic redundancy resolution, as well as robot dynamics, including actuators model. The kinematic redundancy is taken into account through a secondary criterion of joint limits avoidance. The optimization procedure is performed subject to limitations on actuator torques and workspace, while passing through imposed poses. The Augmented Lagrangian with decoupling (ALD) technique is used to solve the resulting constrained non-convex and non-linear optimal control problem. Furthermore, the final state constraint is solved using a gradient projection. Simulations on a three degrees of freedom planar redundant serial manipulator show the effectiveness of the proposed system.

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110027
Author(s):  
Jianqiang Wang ◽  
Yanmin Zhang ◽  
Xintong Liu

To realize efficient palletizing robot trajectory planning and ensure ultimate robot control system universality and extensibility, the B-spline trajectory planning algorithm is used to establish a palletizing robot control system and the system is tested and analyzed. Simultaneously, to improve trajectory planning speeds, R control trajectory planning is used. Through improved algorithm design, a trajectory interpolation algorithm is established. The robot control system is based on R-dominated multi-objective trajectory planning. System stack function testing and system accuracy testing are conducted in a production environment. During palletizing function testing, the system’s single-step code packet time is stable at approximately 5.8 s and the average evolutionary algebra for each layer ranges between 32.49 and 45.66, which can save trajectory planning time. During system accuracy testing, the palletizing robot system’s repeated positioning accuracy is tested. The repeated positioning accuracy error is currently 10−1 mm and is mainly caused by friction and the machining process. By studying the control system of a four-degrees-of-freedom (4-DOF) palletizing robot based on the trajectory planning algorithm, the design predictions and effects are realized, thus providing a reference for more efficient future palletizing robot design. Although the working process still has some shortcomings, the research has major practical significance.


1987 ◽  
Vol 11 (4) ◽  
pp. 197-200 ◽  
Author(s):  
B. Benhabib ◽  
R.G. Fenton ◽  
A.A. Goldenberg

The basic characteristic of kinematically redundant robots is that non-unique joint solutions may exist for a specified end effector location. Thus, trajectory planning for a kinematically redundant robot requires an optimization procedure to determine the joint displacements when solving the inverse kinematics relations. In this paper an analytical solution is developed for the trajectory optimization problem of redundant robots based on the classical Lagrange’s method. A detailed formulation is provided for seven degrees of freedom robots, which minimizes the Euclidean norm of joint dislacements for point-to-point motion trajectory planning.


2020 ◽  
Vol 10 (21) ◽  
pp. 7626
Author(s):  
Clautilde Nguiadem ◽  
Maxime Raison ◽  
Sofiane Achiche

(1) Background: Motion planning is an important part of exoskeleton control that improves the wearer’s safety and comfort. However, its usage introduces the problem of trajectory planning. The objective of trajectory planning is to generate the reference input for the motion-control system. This review explores the methods of trajectory planning for exoskeleton control. In order to reduce the number of surveyed papers, this review focuses on the upper limbs, which require refined three-dimensional motion planning. (2) Methods: A systematic search covering the last 20 years was conducted in Ei Compendex, Inspect-IET, Web of Science, PubMed, ProQuest, and Science-Direct. The search strategy was to use and combine terms “trajectory planning”, “upper limb”, and ”exoskeleton” as high-level keywords. “Trajectory planning” and “motion planning” were also combined with the following keywords: “rehabilitation”, “humanlike motion“, “upper extremity“, “inverse kinematic“, and “learning machine “. (3) Results: A total of 67 relevant papers were discovered. Results were then classified into two main categories of methods to plan trajectory: (i) Approaches based on Cartesian motion planning, and inverse kinematics using polynomial-interpolation or optimization-based methods such as minimum-jerk, minimum-torque-change, and inertia-like models; and (ii) approaches based on “learning by demonstration” using machine-learning techniques such as supervised learning based on neural networks, and learning methods based on hidden Markov models, Gaussian mixture models, and dynamic motion primitives. (4) Conclusions: Various methods have been proposed to plan the trajectories for upper-limb exoskeleton robots, but most of them plan the trajectory offline. The review approach is general and could be extended to lower limbs. Trajectory planning has the advantage of extending the applicability of therapy robots to home usage (assistive exoskeletons); it also makes it possible to mitigate the shortages of medical caregivers and therapists, and therapy costs. In this paper, we also discuss challenges associated with trajectory planning: kinematic redundancy and incompatibility, and the trajectory-optimization problem. Commonly, methods based on the computation of swivel angles and other methods rely on the relationship (e.g., coordinated or synergistic) between the degrees of freedom used to resolve kinematic redundancy for exoskeletons. Moreover, two general solutions, namely, the self-tracing configuration of the joint axis and the alignment-free configuration of the joint axis, which add the appropriate number of extra degrees of freedom to the mechanism, were employed to improve the kinematic incompatibility between human and exoskeleton. Future work will focus on online trajectory planning and optimal control. This will be done because very few online methods were found in the scope of this study.


Author(s):  
Louis-Thomas Schreiber ◽  
Clément Gosselin

This paper presents trajectory planning methods for a kinematically redundant parallel mechanism. The architecture of the mechanism is similar to the well-known Gough-Stewart platform and it retains its advantages, i.e., the members connecting the base to the moving platform are only subjected to tensile/compressive loads. The kinematic redundancy is exploited to avoid singularities and extend the rotational workspace. The architecture is described and the associated kinematic relationships are presented. Solutions for the inverse kinematics are given, as well as strategies to take into account the limitations of the mechanism such as mechanical interferences and velocity limits of the actuators while controlling the redundant degrees of freedom.


2021 ◽  
Vol 45 ◽  
pp. 101111
Author(s):  
Mohammad Hassan Shahverdian ◽  
Ali Sohani ◽  
Hoseyn Sayyaadi ◽  
Saman Samiezadeh ◽  
Mohammad Hossein Doranehgard ◽  
...  

2005 ◽  
Vol 02 (01) ◽  
pp. 105-124 ◽  
Author(s):  
VELJKO POTKONJAK

Handwriting has always been considered an important human task, and accordingly it has attracted the attention of researchers working in biomechanics, physiology, and related fields. There exist a number of studies on this area. This paper considers the human–machine analogy and relates robots with handwriting. The work is two-fold: it improves the knowledge in biomechanics of handwriting, and introduces some new concepts in robot control. The idea is to find the biomechanical principles humans apply when resolving kinematic redundancy, express the principles by means of appropriate mathematical models, and then implement them in robots. This is a step forward in the generation of human-like motion of robots. Two approaches to redundancy resolution are described: (i) "Distributed Positioning" (DP) which is based on a model to represent arm motion in the absence of fatigue, and (ii) the "Robot Fatigue" approach, where robot movements similar to the movements of a human arm under muscle fatigue are generated. Both approaches are applied to a redundant anthropomorphic robot arm performing handwriting. The simulation study includes the issues of legibility and inclination of handwriting. The results demonstrate the suitability and effectiveness of both approaches.


Author(s):  
Ali Thamallah ◽  
Anis Sakly ◽  
Faouzi M’Sahli

This article focuses on the tracking and stabilizing issues of a class of discrete switched systems. These systems are characterized by unknown switching sequences, a non-minimum phase, and time-varying or dead modes. In particular, for those governed by an indeterminate switching signal, it is very complicated to synthesize a control law able to systematically approach general reference-tracking difficulties. Taking into account the difficulty to express the dynamic of this class of systems, the present paper presents a new Dynamic matrix control method based on the multi-objective optimization and the truncated impulse response model. The formulation of the optimization problem aims to approach the general step-tracking issues under persistent and indeterminate mode changes and to overcome the stability problem along with retaining as many desirable features of the standard dynamic matrix control (DMC) method as possible. In addition, the formulated optimization problem integrates estimator variables able to manipulate the optimization procedure in favor of the active mode with an appropriate adjustment. It also provides a progressive and smooth multi-objective control law even in the presence of problems whether in subsystems or switching sequences. Finally, simulation examples and comparison tests are conducted to illustrate the potentiality and effectiveness of the developed method.


Author(s):  
A. Meghdari ◽  
H. Sayyaadi

Abstract An optimization technique based on the well known Dynamic Programming Algorithm is applied to the motion control trajectories and path planning of multi-jointed fingers in dextrous hand designs. A three fingered hand with each finger containing four degrees of freedom is considered for analysis. After generating the kinematics and dynamics equations of such a hand, optimum values of the joints torques and velocities are computed such that the finger-tips of the hand are moved through their prescribed trajectories with the least time or/and energy to reach the object being grasped. Finally, optimal as well as feasible solutions for the multi-jointed fingers are identified and the results are presented.


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