Trajectory Planning Of Manipulators Research Articles

Trajectory Planning, Kinematics, and Experimental Validation of a 3D-Printed Delta Robot Manipulator

This paper presents the implementation, trajectory planning, kinematics, and experimental validation of an open-source 3D-printed delta robot manipulator. The robot’s hardware consists of three servo motors, an Arduino Uno microcontroller, and a Pulse Width Modulation (PWM) servo module. The software includes a trapezoidal velocity profile planner and an inverse and forward kinematics solver to calculate the motor angles required to achieve a desired end-effector position in task space. The 3D printed parts were obtained from an open-source Thingiverse project and assembled to form the robot’s kinematic structure. The robot’s performance was evaluated in terms of its accuracy, repeatability, and maximum speed for a pick-and-place task. Experimental results show that the robot can achieve a positioning accuracy of 2.2 mm, with a top speed of 0.4 m/s, 30 picks per minute, and load carrying capacity up to 200 g. These results are satisfactory, considering the ease of assembly and the cost-effectiveness of the robot. The comparison of the calculated motor angles with actual motor angles obtained through additional potentiometer wires soldering shows promising results. The proposed robot’s cost-effective characteristics, utilization of open-source additive manufacturing, and motion planning algorithms make it suitable for various applications, including education, research, and small-scale industrial applications.

Trajectory planning and control of large robotic excavators based on inclination-displacement mapping

This paper proposes a trajectory planning and control method for heavy-duty manipulators based on inclination-displacement mapping. In this method, inclination sensors are employed to detect the excavator's orientation. By establishing a mapping relationship between joint inclination and cylinder displacement, the cylinder displacement is indirectly derived. Subsequently, considering the typical excavation operation process, the spatial trajectory of the excavator bucket is planned. The displacement of the driving cylinder is determined using kinematic inverse solutions and cubic polynomials. The cylinder displacement is then controlled using a position-velocity (PV) strategy. This method is tested on a 95-ton large excavator, and the results demonstrate several advantages, including easy installation, low maintenance requirements, smooth trajectory planning, and high tracking accuracy. These qualities make it suitable for the demands of intelligent operations in large excavators. Thus, this paper offers valuable insights for the intelligent transformation of heavy excavators.

A Forward Solution Algorithm of 6RUS Parallel Mechanism Based on Dual Quaternion Method

The 6RUS parallel manipulator is a highly versatile and widely used robotic mechanism with six degrees of freedom. Its intricate kinematic structure and its capability to perform complex motion tasks have garnered significant research interest in recent years. The kinematic analysis of the 6RUS mechanism plays a crucial role in understanding its operational characteristics and optimizing its performance for various applications. In this paper, we present a state-of-the-art kinematic algorithm for the 6RUS parallel manipulator. Our algorithm is aimed at addressing the challenges associated with accurately determining the pose and motion of the end-effector relative to the base, considering the complexity of the mechanism’s architecture. By leveraging advanced mathematical modeling techniques and utilizing efficient computational algorithms, our proposed algorithm offers improved accuracy, efficiency, and robustness in determining the kinematic parameters of the 6RUS mechanism. The key contributions of this work include the development of a comprehensive forward and inverse kinematic model for the 6RUS parallel manipulator, incorporating the effects of joint constraints, singularities, and workspace limitations. We also present a detailed analysis of the algorithm’s performance in comparison to existing approaches, demonstrating its superiority in terms of computational efficiency and accuracy. The proposed kinematic algorithm holds significant potential for enhancing the design, control, and trajectory planning of 6RUS parallel manipulators. It provides a solid foundation for advanced applications such as robotic surgery, industrial automation, and virtual reality systems. The results presented in this paper contribute to the growing body of knowledge in parallel manipulator research and pave the way for future developments in the field.

Optimal Trajectory Planning of an Omni-directional Mobile Manipulator for Obstacle Avoidance

Optimal Trajectory Planning of an Omni-directional Mobile Manipulator for Obstacle Avoidance

Space Manipulator Collision Avoidance Using a Deep Reinforcement Learning Control

Recent efforts in on-orbit servicing, manufacturing, and debris removal have accentuated some of the challenges related to close-proximity space manipulation. Orbital debris threatens future space endeavors driving active removal missions. Additionally, refueling missions have become increasingly viable to prolong satellite life and mitigate future debris generation. The ability to capture cooperative and non-cooperative spacecraft is an essential step for refueling or removal missions. In close-proximity capture, collision avoidance remains a challenge during trajectory planning for space manipulators. In this research, a deep reinforcement learning control approach is applied to a three-degrees-of-freedom manipulator to capture space objects and avoid collisions. This approach is investigated in both free-flying and free-floating scenarios, where the target object is either cooperative or non-cooperative. A deep reinforcement learning controller is trained for each scenario to effectively reach a target capture location on a simulated spacecraft model while avoiding collisions. Collisions between the base spacecraft and the target spacecraft are avoided in the planned manipulator trajectories. The trained model is tested for each scenario and the results for the manipulator and base motion are detailed and discussed.

Trajectory planning of large redundant manipulator considering kinematic constraints and energy efficiency

AbstractFor the large redundant manipulator, due to its long working distance and large mass, the number of links (i.e., manipulator’s arms) that can be driven to move simultaneously is limited. Otherwise, the control accuracy and motion stability of the manipulator will deteriorate. Focusing on that, a weighted Newton iteration (WNI) algorithm for trajectory planning of the manipulator is firstly proposed, where the motion of the manipulator joints is controlled by a weight matrix, which is constant and related to each link’s energy consumption. To dynamically adjust the weight matrix according to kinematic constraints and acquire better energy efficiency, an adaptive WNI (AWNI) algorithm is further proposed. In AWNI, the weight matrix is adjusted in real-time during the planning process, with considerations of the kinematic constraints and the energy consumption of the manipulator. The switch of the links between the working state and the non-working state is made through the weight matrix to achieve flexible control of the manipulator motion. Two evaluation functions are established to validate the effectiveness of AWNI in energy saving and motion stability control. Taking a 6 degrees of freedom (DOF) manipulator as an example, simulation experiments on trajectory planning are carried out and the results show the effectiveness of the proposed AWNI algorithm.

Trajectory planning and control algorithm of industrial robot manipulator

As the industrial robot task becomes more complex, the difficulty of trajectory planning and tracking control of manipulator is gradually increasing. To minimize the vibration during the manipulator motion and improve the planning accuracy, the method of quintic polynomial combined with non-uniform B-spline interpolation is studied for joint space (JS) planning. The trajectory tracking system is easily affected by friction nonlinearity and parameters. So a JS trajectory tracking controller based on based on fuzzy neural network (FNN) is designed. Through simulation experiments, the curve obtained by the planning method studied is smoother and the planning error is minimum. The maximum position error is 0.09 rad, and the speed error is not more than 0.1 rad/s. The controller performance test results under different parameters show that the W^, c^, κ^ parameter in FNN can be adjusted in real time, and the value will not affect the performance of the controller. The fluctuation range of trajectory error of different joints is within ±0.2×10-5rad, which indicates that the performance of AFNNC controller studied is better. And its response time is the shortest and its robustness is better when the load changes suddenly.

Trajectory Planning for Mobile Manipulators with Control Constraints

This paper presents the method of trajectory planning for mobile manipulators considering limitations resulting from capabilities of robotic system actuators. The fulfillment of control constraints is achieved by introducing virtual control scaling of the robot trajectory in the limited periods of time. Such an approach allows researchers to obtain the trajectories fulfilling control constraints without significantly increasing the time of task execution. The proposed method generates sub-optimal trajectories maximizing the manipulability measure of the robot arm, preserves mechanical and collision avoidance limitations and can be used in real-time trajectory planning. The effectiveness of the presented solution is confirmed by computer simulations involving a mobile manipulator with parameters corresponding to KUKA youBot.

An Analysis Review: Optimal Trajectory for 6-DOF-based Intelligent Controller in Biomedical Application

With technological advancements and the development of robots have begun to be utilized in numerous sectors, including industrial, agricultural, and medical. Optimizing the path planning of robot manipulators is a fundamental aspect of robot research with promising future prospects. The precise robot manipulator tracks can enhance the efficacy of a variety of robot duties, such as workshop operations, crop harvesting, and medical procedures, among others. Trajectory planning for robot manipulators is one of the fundamental robot technologies, and manipulator trajectory accuracy can be enhanced by the design of their controllers. However, the majority of controllers devised up to this point were incapable of effectively resolving the nonlinearity and uncertainty issues of high-degree freedom manipulators in order to overcome these issues and enhance the track performance of high-degree freedom manipulators. Developing practical path-planning algorithms to efficiently complete robot functions in autonomous robotics is critical. In addition, designing a collision-free path in conjunction with the physical limitations of the robot is a very challenging challenge due to the complex environment surrounding the dynamics and kinetics of robots with different degrees of freedom (DoF) and/or multiple arms. The advantages and disadvantages of current robot motion planning methods, incompleteness, scalability, safety, stability, smoothness, accuracy, optimization, and efficiency are examined in this paper.

Deep Reinforcement Learning With a Stage Incentive Mechanism of Dense Reward for Robotic Trajectory Planning

To improve the efficiency of deep reinforcement learning (DRL)-based methods for robot manipulator trajectory planning in random working environments, we present three dense reward functions. These rewards differ from the traditional sparse reward. First, a posture reward function is proposed to speed up the learning process with a more reasonable trajectory by modeling the distance and direction constraints, which can reduce the blindness of exploration. Second, a stride reward function is proposed to improve the stability of the learning process by modeling the distance and movement distance of joint constraints. Finally, in order to further improve learning efficiency, we are inspired by the cognitive process of human behavior and propose a stage incentive mechanism, including a hard-stage incentive reward function and a soft-stage incentive reward function. Extensive experiments show that the soft-stage incentive reward function is able to improve the convergence rate, get higher mean reward and lower standard deviation after convergence.

Trajectory Planning for Coal Gangue Sorting Robot Tracking Fast-Mass Target under Multiple Constraints.

Aiming at the problems of grab failure and manipulator damage, this paper proposes a dynamic gangue trajectory planning method for the manipulator synchronous tracking under multi-constraint conditions. The main reason for the impact load is that there is a speed difference between the end of the manipulator and the target when the manipulator grabs the target. In this method, the mathematical model of seven-segment manipulator trajectory planning is constructed first. The mathematical model of synchronous tracking of dynamic targets based on a time-minimum manipulator is constructed by taking the robot's acceleration, speed, and synchronization as constraints. The model transforms the multi-constraint-solving problem into a single-objective-solving problem. Finally, the particle swarm optimization algorithm is used to solve the model. The calculation results are put into the trajectory planning model of the manipulator to obtain the synchronous tracking trajectory of the manipulator. Simulation and experiments show that each joint of the robot's arm can synchronously track dynamic targets within the constraint range. This method can ensure the synchronization of the position, speed, and acceleration of the moving target and the target after tracking. The average position error is 2.1 mm, and the average speed error is 7.4 mm/s. The robot has a high tracking accuracy, which further improves the robot's grasping stability and success rate.

An Optimal Control Approach to the Minimum-Time Trajectory Planning of Robotic Manipulators

Trajectory planning is a classic problem in robotics, with different approaches and optimisation objectives documented in the literature. Most of the time, the path is assumed, i.e., pre-defined, and optimisation consists of finding the timing of motion under a number of constraints. The focus of this work is on the minimum-time manoeuvring of robotic manipulators. A nonlinear optimal control approach is proposed that does not require the provision of either a pre-defined path or a pre-defined control structure and allows the inclusion of dynamic constraints. The solution (path and timing of motion) is obtained by transforming the optimal control problem into a nonlinear programming problem. The proposed approach is applied to a two-link manipulator for illustration purposes. The optimisation is carried out both without and with obstacles. The minimum-distance and minimum-time solutions are compared, and some classic results are obtained, including the trapezoidal pattern of the joint velocity and the bang–bang structure of the control torques. The effects of limitations on the jerks of actuators and the rate of change in torque inputs are discussed. The application to a four-link manipulator is also included to show the ‘scalability’ of the approach, together with a comparison with a classic path-and-motion-planning method, to highlight the characteristics and performance of the proposed approach. Finally, the possibility of enforcing a number of via-points along the path is demonstrated. The proposed method allows the computation of the path and motion simultaneously with the computation time, which is 1–30 times the manoeuvre time, on a standard PC with the current implementation.

Vibration Suppression Trajectory Planning of Underwater Flexible Manipulators Based on Incremental Kriging-Assisted Optimization Algorithm

It is of great significance to expand the functions of submarines by carrying underwater manipulators with a large working space. To suppress the flexible vibration of underwater manipulators, an improved sparrow search algorithm (ISSA) combining an elite strategy and a sine algorithm is proposed for the trajectory planning of underwater flexible manipulators. In this method, the vibration evaluation function is established based on the precise dynamic model of the underwater flexible manipulator and considering complex motion and vibration constraints. Simulation results show that the ISSA algorithm requires only 1/3.68 of the time of PSO. Compared to PSO, SSA and the opposition-based learning sparrow search algorithm (OBLSSA), the optimization performance is improved by 17.3%, 13.1% and 9.7%, respectively. However, because the complex dynamics model of the underwater flexible manipulator leads to large computational effort and a long optimization time, ISSA is difficult to apply directly in practice. To obtain a large number of optimization results in a shorter time, an incremental Kriging-assisted ISSA (IKA-ISSA) is proposed in this paper. Simulation results show that IKA-ISSA has good nonlinear approximation ability and the optimization time is only 3% of that of the ISSA.

An Incremental Inverse Reinforcement Learning Approach for Motion Planning with Separated Path and Velocity Preferences

Humans often demonstrate diverse behaviors due to their personal preferences, for instance, related to their individual execution style or personal margin for safety. In this paper, we consider the problem of integrating both path and velocity preferences into trajectory planning for robotic manipulators. We first learn reward functions that represent the user path and velocity preferences from kinesthetic demonstration. We then optimize the trajectory in two steps, first the path and then the velocity, to produce trajectories that adhere to both task requirements and user preferences. We design a set of parameterized features that capture the fundamental preferences in a pick-and-place type of object transportation task, both in the shape and timing of the motion. We demonstrate that our method is capable of generalizing such preferences to new scenarios. We implement our algorithm on a Franka Emika 7-DoF robot arm and validate the functionality and flexibility of our approach in a user study. The results show that non-expert users are able to teach the robot their preferences with just a few iterations of feedback.

Research on Configuration Design Optimization and Trajectory Planning of Manipulators for Precision Machining and Inspection of Large-Curvature and Large-Area Curved Surfaces.

In recent years, high-quality surfaces with large areas and curvatures have been increasingly used in engineering, but the precision machining and inspection of such surfaces is a particular challenge. Surface machining equipment needs to have a large working space, high flexibility, and motion accuracy to meet the demands of micron-scale precision machining. However, meeting these requirements may result in extremely large equipment sizes. To solve this problem, an eight-degree-of-freedom redundant manipulator with one linear and seven rotational joints is designed to assist in the machining described in this paper. The configuration parameters of the manipulator are optimized by an improved multi-objective particle swarm optimization algorithm to ensure that the working space of the manipulator completely covers the working surface and that the size of the manipulator is small. In order to improve the smoothness and accuracy of manipulator motion on large surface areas, an improved trajectory planning strategy for a redundant manipulator is proposed. The idea of the improved strategy is to pre-process the motion path first and then use a combination of the clamping weighted least-norm method and the gradient projection method to plan the trajectory, while adding a reverse planning step to solve the singularity problem. The resulting trajectories are smoother than those planned by the general method. The feasibility and practicality of the trajectory planning strategy are verified through simulation.

Knowledge Database-Based Multiobjective Trajectory Planning of 7-DOF Manipulator With Rapid and Continuous Response to Uncertain Fast-Flying Objects

The problems of a 7-degree of freedom (DOF) manipulator with rapid and continuous response to uncertain fast-flying objects are addressed: 1) how to effectively solve trajectory planning of the 7-DOF manipulator with multiple criteria; and 2) how to make the 7-DOF manipulator realize the rapid and continuous response to uncertain fast-flying objects. In the proposed approach, based on the trajectory parameterization of the 7-DOF manipulator, a multiobjective teaching-learning-based optimization (MOTLBO) algorithm is adopted to find a close representation of the Pareto optimal set rather than a single solution. As such, an optimal solution can be chosen as digital knowledge information. A new methodology based on a knowledge base representing and learning the operation environment, that is, skill digitization, is presented, which enables the 7-DOF manipulator to realize the rapid and continuous response skill. Simulation and practical testing results of a ping-pong robot validate the feasibility and effectiveness of the proposed approach, in which the online trajectory generation spends only around 1 ms.

Research on trajectory planning of mobile manipulator based on improved gradient projection algorithm

This paper takes a 10 DOF mobile manipulator as the research object. Aiming at the problem of joint acceleration overrun in the trajectory planning of a 10 DOF Manipulator, firstly, the scale factor is obtained by the extremum method. Compared with the commonly used extremum method, the optimization degree and the self motion limit factor are introduced, and a new algorithm considering joint acceleration constraint is deduced and proposed. By comparing the simulation results of the inverse solution algorithm, the effectiveness of the new algorithm is verified. Finally, it is applied to a mobile manipulator with 10 degrees of freedom for example motion test. The test results meet the design requirements. The results will be actually applied in engineering projects.

Time-Optimal Asymmetric S-Curve Trajectory Planning of Redundant Manipulators under Kinematic Constraints

This paper proposes a novel trajectory planning algorithm to design an end-effector motion profile along a specified path. An optimization model based on the whale optimization algorithm (WOA) is established for time-optimal asymmetrical S-curve velocity scheduling. Trajectories designed by end-effector limits may violate kinematic constraints due to the non-linear relationship between the operation and joint space of redundant manipulators. A constraints conversion approach is proposed to update end-effector limits. The path can be divided into segments at the minimum of the updated limitations. On each path segment, the jerk-limited S-shaped velocity profile is generated within the updated limitations. The proposed method aims to generate end-effector trajectory by kinematic constraints which are imposed on joints, resulting in efficient robot motion performance. The WOA-based asymmetrical S-curve velocity scheduling algorithm can be automatically adjusted for different path lengths and start/end velocities, allowing flexibility in finding the time-optimal solution under complex constraints. Simulations and experiments on a redundant manipulator prove the effect and superiority of the proposed method.

Dynamic obstacle avoidance and trajectory planning of five-axis redundant industrial manipulator

Aiming at the problem that five axis redundant industrial manipulator dynamic obstacle avoidance and trajectory planning algorithm does not consider the minimum difference of each joint of the manipulator, which leads to low success rate of obstacle avoidance planning, slow convergence speed of path cost and long time of obstacle avoidance planning, a simulation study on dynamic obstacle avoidance trajectory planning of five axis redundant industrial manipulator is proposed. According to the D-H rule, the coordinate system of each link joint of the five axis redundant industrial manipulator is established, and the forward and inverse kinematics of the five axis redundant industrial manipulator is analyzed. AABB's hierarchical bounding box tree algorithm is used to detect the collision of five axis redundant industrial manipulator. This paper uses harmony search algorithm to plan the obstacle avoidance path of five axis redundant industrial manipulator, determines the objective function and constraints of the optimization problem, sets algorithm parameters, initializes harmony memory, creates new harmony, updates harmony memory, checks and searches the target state, achieves the maximum number of iterations, and realizes the dynamic obstacle avoidance and trajectory planning of five axis redundant industrial manipulator. The experimental results show that the path cost of the proposed algorithm converges faster, and can effectively improve the success rate of obstacle avoidance planning and shorten the time of obstacle avoidance planning.

Time-Optimal Trajectory Planning of Flexible Manipulator Moving along Multi-Constraint Continuous Path and Avoiding Obstacles

To solve the trajectory planning problem of the flexible manipulator under various constraints such as end-camera attitude, drive space, and obstacles during video inspection along a continuous path in narrow three-dimensional space, this paper proposes a time-optimal trajectory planning method from the initial configuration to the final configuration. The trajectory planning problem is transformed into a multi-constraint optimization problem. First, to realize continuous video inspection in an unstructured complex environment, by analyzing the geometric model of the two-segment flexible manipulator with a camera at the end, the pose constraints between the camera and the shooting surface are formulated by the space vector method, the driving constraints are formulated based on kinematics, and the obstacle constraints are formulated by space mapping. Then, a multi-constraint optimization model is constructed to generate the smooth trajectory of the drive cable of the flexible manipulator by minimizing the total time of continuous path motion. Compared with the conventional point-to-point collision avoidance planning solution method, this paper starts from the global perspective and investigates the less considered continuous path trajectory planning problem; also, the swarm intelligence algorithm artificial jellyfish search algorithm (JS) is employed to optimize the solution and find the minimum time trajectory conforming to a variety of complex constraints. Finally, a simulation is conducted with CoppeliaSim, and the continuous path video inspection experiment is carried out in the 500KV GIS (Gas Insulated Switchgear) equipment, the simulation and experimental results indicate that the planned drive cable trajectory is smooth and effective. In addition, each path point is tracked and obstacles are avoided safely. When the flexible manipulator moves along the whole path, the pose of the camera satisfies the relaxed attitude constrain The proposed method can guide the two-segment flexible manipulator to complete the continuous video inspection task of the GIS cavity wall and conductive column surface.