Path In Cartesian Space Research Articles

Multi-objective optimal trajectory planning for robot manipulator attention to end-effector path limitation

Abstract In the process of trajectory optimization for robot manipulator, the path that is generated may deviate from the intended path because of the adjustment of trajectory parameters, if there is limitation of end-effector path in Cartesian space for specific tasks, this phenomenon is dangerous. This paper proposes a methodology that is based on the Pareto front to address this issue, and the methodology takes into account both the multi-objective optimization of robotic arm and the quality of end-effector path. Based on dung beetle optimizer, this research proposes improved non-dominated sorting dung beetle optimizer. This paper interpolates manipulator trajectory with quintic B-spline curves, achieves multi-objective trajectory optimization that simultaneously optimizes traveling time, energy consumption, and mean jerk, proposes a trajectory selection strategy that is based on Pareto solution set by introducing the concept of Fréchet distance, and the strategy enables the end-effector to approach the desired path in Cartesian space. Simulation and experimental results validate the effectiveness and practicability of the proposed methodology on the Sawyer robot manipulator.

Time-Optimal Trajectory Planning of 6-DOF Manipulator Based on Fuzzy Control

Currently, the teaching programming or offline programming used by an industrial manipulator can manually set the running speed of the manipulator. In this paper, to consider the running speed and stability of the manipulator, the time-optimal trajectory planning (TOTP) of the manipulator is transformed into a nonlinear optimal value search problem under multiple constraints, and a time-search algorithm based on fuzzy control is proposed, so that the end of the manipulator can run along the given path in Cartesian space for the shortest time, and the angular velocity and angular acceleration of each joint is within a limited range. In addition, a simulation model of a 6-DOF manipulator is established in MATLAB, taking a straight-line trajectory of the end of the manipulator in Cartesian space as an example, and the effectiveness and efficiency of the algorithm proposed in this paper are proved by comparing the execution time with the bisection algorithm and the traditional gradient descent method.

A General Framework of Motion Planning for Redundant Robot Manipulator Based on Deep Reinforcement Learning

Motion planning and its optimization is vital and difficult for redundant robot manipulator in an environment with obstacles. In this article, a general motion planning framework that integrates deep reinforcement learning (DRL) is proposed to explore the length-optimal path in Cartesian space and to derive the energy-optimal solution to inverse kinematics. First, based on the maximum entropy framework and Tsallis entropy, a DRL algorithm with clipped automatic entropy adjustment is proposed to make the agent to be qualified to cope with diverse tasks. Second, a path planning structure that combines traditional path planner and DRL is proposed, which integrates the powerful exploration capability of the former and exploitation of experience replay of the latter to enhance the planning performance. Third, based on the exploration ability of DRL and the nonlinear fitting ability of artificial neural networks, a structure is proposed to provide an energy-optimal inverse kinematics solution for redundant robot manipulators. Finally, experimental results on both simulated and real-world customized scenarios have verified the performance of the proposed work.

Spot-welding path planning method for the curved surface workpiece of body-in-white based on a memetic algorithm

Aiming at the problem of complex path planning in the processing of curved surface workpieces of body-in-white, a hybrid path planning method based on a memetic algorithm is proposed. The method is divided into two parts: welding sequence planning and welding path planning between weld points. By establishing the kinematic model of a spot welding robot based on the pipper criterion and z-y-z Euler angle solution method, the motion constraints of path optimization are analyzed. Under the framework of the memetic algorithm, the improved A-star algorithm with redundant node deletion and a post-smoothing process is used to obtain the smooth collision-free optimal path set between weld points and to construct the objective function of travelling all weld points with the shortest path length and highest smoothness. The multiobjective elitist-simulated annealing genetic algorithm (MESAGA) is used to achieve the welding sequence planning of all weld points. The variable neighborhood search method improves the mutation operator; the elitist strategy is introduced to improve the probability of elitist individual crossover and mutation operation, and a simulated annealing algorithm is used to jump out of local search to obtain the global optimal solution. According to the motion constraints, the joint space path is obtained by the optimal path in Cartesian space. Simulation analysis results demonstrate that the hybrid path planning method based on the memetic algorithm can effectively optimize the path of spot welding robots and lay the foundation for control and trajectory planning during welding processes.

Switched visual servo control of nonholonomic mobile robots with field-of-view constraints based on homography

This paper presents a novel scheme for visual servoing of a nonholonomic mobile robot equipped with a monocular camera in consideration of field-of-view (FOV) constraints. In order to loosen the FOV constraints, the system states are expressed by the homography between the current frame and the key frame so that the target is not necessarily to be always visible in the control process. A switched visual controller is designed to deal with the nonholonomic constraints. Moreover, an iteration strategy is used to eliminate errors caused by the parameter uncertainty. The stablity and robustness of the proposed scheme are guaranteed by theoretical analysis. Compared to conventional schemes, the proposed approach has the following advantages: 1) a better path in Cartesian space can be achieved owing to the loosening of FOV constraints; 2) the iteration strategy ensures the robustness to parameter uncertainty; 3) when used in landmark-based navigation, it needs much sparser and simpler landmarks than those localization-based approaches need. Simulation results demonstrate the effectiveness of the proposed method.

Admittance-Based Upper Limb Robotic Active and Active-Assistive Movements

This paper presents two rehabilitation schemes for patients with upper limb impairments. The first is an active-assistive scheme based on the trajectory tracking of predefined paths in Cartesian space. In it, the system allows for an adjustable degree of variation with respect to ideal tracking. The amount of variation is determined through an admittance function that depends on the opposition forces exerted on the system by the user, due to possible impairments. The coefficients of the function allow the adjustment of the degree of assistance the robot will provide in order to complete the target trajectory. The second scheme corresponds to active movements in a constrained space. Here, the same admittance function is applied; however, in this case, it is unattached to a predefined trajectory and instead connected to one generated in real time, according to the user's intended movements. This allows the user to move freely with the robot in order to track a given path. The free movement is bounded through the use of virtual walls that do not allow users to exceed certain limits. A human-machine interface was developed to guide the robot's user.

Development of a neural controller applied in a 5 DOF robot redundant

In this paper the development of a neural controller implemented in a five Degrees Of Freedom (DOF) redundant robot is presented. The design of the control law considers the robotic system inverse model, including the performance of the actuators for the five joints, obtained through a feedforward neural network with backpropagation learning algorithm. This inverse structure is weighted by desired acceleration and derivative proportional feedback loops to provide the appropriate supply voltage to the servo motors of the robotic manipulator. Tracking tests are performed to a path in Cartesian space using a simulator developed using MatLab/Simulink software tools. It assesses the neural controller performance versus classical computed torque controller, comparing the results of curves in the joint space and Cartesian through RMS errors indices of Cartesian and joint positions.

String method for calculation of minimum free-energy paths in Cartesian space in freely-tumbling systems.

The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string.

The Trajectory Planning of Robotic Operation Simulation Based on Virtual Reality

At present, robot simulation based on virtual reality is a hot spot in the study of the robotic. We can build more intuitive and efficient and realistic simulation environment of processing of the robot through combining computer technology and virtual reality technology to carry out a more effective human-machine interactive operation. Robotic trajectory planning is not only the basis of trajectory tracking control, but also the implementation of tasks in robotics. It is discussed trajectory planning and path generation based on robot kinematics and dynamics in the joint space and Cartesian space. In this paper, we study the robot trajectory planning and use three B-spines fitting the robot path in Cartesian space.

Optimized Torsion-Angle Normal Modes Reproduce Conformational Changes More Accurately Than Cartesian Modes

We present what to our knowledge is a new method of optimized torsion-angle normal-mode analysis, in which the normal modes move along curved paths in Cartesian space. We show that optimized torsion-angle normal modes reproduce protein conformational changes more accurately than Cartesian normal modes. We also show that orthogonalizing the displacement vectors from torsion-angle normal-mode analysis and projecting them as straight lines in Cartesian space does not lead to better performance than Cartesian normal modes. Clearly, protein motion is more naturally described by curved paths in Cartesian space.

Continuous Genetic Algorithms for Collision-Free Cartesian Path Planning of Robot Manipulators

A novel continuous genetic algorithm (CGA) along with distance algorithm for solving collisions-free path planning problem for robot manipulators is presented in this paper. Given the desired Cartesian path to be followed by the manipulator, the robot configuration as described by the D-H parameters, and the available stationary obstacles in the workspace of the manipulator, the proposed approach will autonomously select a collision free path for the manipulator that minimizes the deviation between the generated and the desired Cartesian path, satisfy the joints limits of the manipulator, and maximize the minimum distance between the manipulator links and the obstacles. One of the main features of the algorithm is that it avoids the manipulator kinematic singularities due to the inclusion of forward kinematics model in the calculations instead of the inverse kinematics. The new robot path planning approach has been applied to two different robot configurations; 2R and PUMA 560, as non-redundant manipulators. Simulation results show that the proposed CGA will always select the safest path avoiding obstacles within the manipulator workspace regardless of whether there is a unique feasible solution, in terms of joint limits, or there are multiple feasible solutions. In addition to that, the generated path in Cartesian space will be of very minimal deviation from the desired one.

Onsager–Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways

For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system, a path in Cartesian space is transformed into that in Fourier space, and an overdamped Langevin equation is derived for the Fourier components to achieve a canonical ensemble of the path at a finite temperature. To avoid "path trapping" around an initially guessed path, the path sampling method is further combined with a powerful sampling technique, the replica exchange method. The principle and algorithm of our method is numerically demonstrated for a model two-dimensional system with a bifurcated potential landscape. The results are compared with those of conventional transition path sampling and the equilibrium theory, and the error due to path discretization is also discussed.

Fuzzy improved adaptive neuro-NMPC for online path tracking and obstacle avoidance of redundant robotic manipulators

This paper presents a non-linear model predictive control (NMPC) for redundant robotic manipulators. Using NMPC, the end-effector of the robotic manipulator tracks a predefined geometry path in Cartesian space in such a way that no collision with obstacles in the workspace and no singular configurations for the robot occurs. Non-linear dynamic of the robot, including actuators dynamic, is also considered. Moreover, the online tuning of the weights in NMPC is performed using the fuzzy logic. The proposed method automatically adjusts the weights in the cost function in order to obtain good performance. Furthermore, using neural networks for model prediction, no prior knowledge about system parameters is necessary and system robustness against changes in its parameters is achieved. Numerical simulations of a 4DOF redundant spatial manipulator actuated by DC servomotors show effectiveness of the proposed method.

Optimization-based trajectory planning of the human upper body

This paper presents studies of the coordination of human upper body voluntary movement. A minimum-jerk 3D model is used to obtain the desired path in Cartesian space, which is widely used in the prediction of human reach movement. Instead of inverse kinematics, a direct optimization approach is used to predict each joint's profile (a spline curve). This optimization problem has four cost function terms: (1) Joint displacement function that evaluates displacement of each joint away from its neutral position; (2) Inconsistency function, which is the joint rate change (first derivative) and predicted overall trend from the initial target point to the final target point; (3) The non-smoothness function of the trajectory, which is the second derivative of the joint trajectory; (4) The non-continuity function, which consists of the amplitudes of joint angle rates at the initial and final target points, in order to emphasize smooth starting and ending conditions. This direct optimization technique can be used for potentially any number of degrees of freedom (DOF) system and it reduces the cost associated with certain inverse kinematics approaches for resolving joint profiles. This paper presents a high redundant upper-body modeling with 15 DOFs. Illustrative examples are presented and an interface is set up to visualize the results.

산업용로봇 작업을 위한 유연한 연결경로 생성과 시간계획

This article proposes a smooth path generation and time scheduling method for general tasks defined by non-smooth path segments in industrial robotic applications. This method utilizes a simple 3rd order polynomial function for smooth interpolation between non-smooth path segments, so that entire task can effectively maintain constant line speed of operation. A predictor-corrector type numerical mapping technique, which correlates time based speed profile to the smoothed path in Cartesian space, is also provided. Finally simulation results show the feasibility of the proposed algorithm.

Real-time accurate hand path tracking and joint trajectory planning for industrial robots(II)

Previously, researchers raised the accuracy for a robot’s hand to track a specified path in Cartesian space mainly through increasing the number of knots on the path and the number of the path’s segments, which results in the heavier online computational burden for the robot controller. Aiming at overcoming this drawback, the authors propose a new kind of real-time accurate hand path tracking and joint trajectory planning method. Through selecting some extra knots on the specified hand path by a certain rule and introducing a sinusoidal function to the joint displacement equation of each segment, this method can greatly raise the path tracking accuracy of robot’s hand and does not change the number of the path’s segments. It also does not increase markedly the computational burden of robot controller. The result of simulation indicates that this method is very effective, and has important value in increasing the application of industrial robots.

Trajectory adaptation to a nonlinear visuomotor transformation: evidence of motion planning in visually perceived space

1. Although reaching movements are characterized by hand paths that tend to follow roughly straight lines in Cartesian space, a fundamental issue is whether this reflects constraints associated with perception or movement production. 2. To address this issue, we examined two-joint planar reaching movements in which we manipulated the mapping between actual and visually perceived motion. In particular, we used a nonlinear transformation such that straight line hand paths in Cartesian space would result in curved paths in perceived space and vice versa. 3. Under these conditions, subjects learned to make straight line paths in perceived space even though the paths of the hand in Cartesian space were markedly curved. In contrast, when the motion was perceived in Cartesian space (i.e., in the absence of a nonlinear distortion), straight line hand paths were observed. 4. These findings suggest that visually guided reaching movements are planned in a perceptual frame of reference. Reaching movements in the horizontal plane are adapted so as to produce straight lines in visually perceived space.

A parallel algorithm for generating set points in cartesian space for spline motion

Abstract A new method for the planning of the position and orientation of an end‐effector along a spline path in Cartesian space is presented. The method is developed using parallel computation. This parallel algorithm for path planning is a function of Cartesian displacement which is determined by the system's speed profile. In positional path planning, the algorithm interpolates a spline path directly based on the circular arc generation method instead of composing piecewise‐straight line segments. In rotational path planning, the algorithm eliminates the wobbling approach vector which conventional methods had suffered. When initial data is determined, position and orientation of the end‐effector can be computed in parallel. If the algorithm is executed by three processors, the computational time is reduced by a factor of 1.67. For four and eight processors, the computational time is further reduced by a factor of 2.0 and 2.22, respectively. When the straight line case of the scheme is executed serially, the computing time is about two thirds of that of the conventional method. An example implemented in a UNIX system shows that the algorithm elegantly solves the problem of the wobbling approach vector.

The near time-optimal motion control of robotic manipulators

The development of strategies for near time-optimal motion control of robotic manipulators is discussed. A PUMA 560 three degree-of-freedom industrial robot is used for computer simulation of algorithm. A quintic polynomial describes the trajectory of the robot end-effector traversing a specified path in Cartesian space. It is shown that a significant increase in speed and accuracy of the manipulator can be achieved with the use of the proposed algorithm.