Joint Space Trajectory Research Articles

Direct Trajectory Optimization of Free-Floating Space Manipulator for Reducing Spacecraft Variation

This letter investigates the direct trajectory optimization of the free-floating space manipulator (FFSM). The main purpose is to plan the joint space trajectories to reduce the spacecraft motion due to the joint rotation during the FFSM performing tasks. To improve the calculation efficiency, the adaptive Radau pseudospectral method (A-RPM) is applied to discretize the system dynamics and transform the formulated optimal problem into a nonlinear programming problem (NLP). By adaptively subdividing the current segment and assigning collocation points according to the solution error, high-degree interpolation polynomials are avoided. To verify the effectiveness of the proposed method, a ground micro-gravity platform of the FFSM system is designed by using the air-bearing technique, on which experiments are carried out. The results show that the variation of the base spacecraft is dramatically reduced if the joints rotate along the optimized trajectories.

Workspace Solution and Space Trajectory Planning of 5-DOF Manipulator

In this paper, a 5-DOF manipulator is designed to carry the pipeline robot. The joint coordinate system and connecting rod parameters of the manipulator are confirmed by D-H method, and the kinematics model of the manipulator is established. The position and direction of the end of the manipulator are deduced by using the homogeneous transformation method. Monte Carlo method is used to solve the workspace of manipulator, and MATLAB is used to draw the workspace cloud map. Set the motion trajectory of manipulator, using joint space trajectory planning, through MATLAB simulation of motion form, get the change of joint. It provides a foundation for trajectory planning, dynamics analysis, motion control and parameter optimization of manipulator.

Dynamic Simulation Modeling of Industrial Robot Kinematics in Industry 4.0

This paper studies the kinematic dynamic simulation modeling of industrial robots in the Industry 4.0 environment and guides the kinematic dynamic simulation modeling of industrial robots in the Industry 4.0 environment in the context of the research. To address the problem that each parameter error has different degrees of influence on the end position error, a method is proposed to calculate the influence weight of each parameter error on the end position error based on the MD-H error model. The error model is established based on the MD-H method and the principle of differential transformation, and then the function of uniform variation of six joint angles with time t is constructed to ensure that each linkage geometric parameter is involved in the motion causing error accumulation. Through the analysis of the robot marking process, the inverse solution is optimized for multiple solutions, and a unique engineering solution is obtained. Linear interpolation, parabolic interpolation, polynomial interpolation, and spline curve interpolation are performed on the results after multisolution optimization in the joint angle, and the pros and cons of various interpolation results are analyzed. The trajectory planning and simulation of industrial robots in the Industry 4.0 environment are carried out by using a special toolbox. The advantages and disadvantages of the two planning methods are compared, and the joint space trajectory planning method is selected to study the planning of its third and fifth polynomials. The kinetic characteristics of the robot were simulated and tested by experimental methods, and the reliability of the simulation results of the kinetic characteristics was verified. The kinematic solutions of industrial robots and the results of multisolution optimization are simulated. The methods, theories, and strategies studied in this paper are slightly modified to provide theoretical and practical support for another dynamic simulation modeling of industrial robot kinematics with various geometries.

Reinforcement Learning-Based Cascade Motion Policy Design for Robust 3D Bipedal Locomotion

This paper presents a novel reinforcement learning (RL) framework to design cascade feedback control policies for 3D bipedal locomotion. Existing RL algorithms are often trained in an end-to-end manner or rely on prior knowledge of some reference joint or task space trajectories. Unlike these studies, we propose a policy structure that decouples the bipedal locomotion problem into two modules that incorporate the physical insights from the nature of the walking dynamics and the well-established Hybrid Zero Dynamics approach for 3D bipedal walking. As a result, the overall RL framework has several key advantages, including lightweight network structure, sample efficiency, and less dependence on prior knowledge. The proposed solution learns stable and robust walking gaits from scratch and allows the controller to realize omnidirectional walking with accurate tracking of the desired velocity and heading angle. The learned policies also perform robustly against various adversarial forces applied to the torso and walking blindly on a series of challenging and unstructured terrains. These results demonstrate that the proposed cascade feedback control policy is suitable for navigation of 3D bipedal robots in indoor and outdoor environments.

Haptic Rendering of Arbitrary Serial Manipulators for Robot Programming

The programming of manipulators is a common task in robotics, for which numerous solutions exist. In this work, a new programming method related to the common master-slave approach is introduced, in which the master is replaced by a digital twin created through haptic and visual rendering. To achieve this, we present an algorithm that enables the haptic rendering of any programmed robot with a serial manipulator on a general-purpose haptic interface. The results show that the proposed haptic rendering reproduces the kinematic properties of the programmed robot and directly provides the desired joint space trajectories. In addition to a stand-alone usage, we demonstrate that the proposed algorithm can be easily paired with existing visual technology for virtual and augmented reality to facilitate a highly immersive programming experience.

Kinematics Analysis and Trajectory Planning Computer Simulation of Smart Apple Bagging Robot by Hail Suppression

In view of the high labor intensity and low efficiency of artificial anti hail apple bagging work, it needs a lot of manpower and financial resources. Therefore, Gansu Zede Electronic Technology Co., Ltd. research and development suitable for the actual production of anti hail apple bagging robot has broad application prospects. In this paper, the kinematics model is established based on the standard matrix representation, and the forward kinematics and inverse kinematics of the anti hail apple bagging robot manipulator are solved and analyzed, and the robot toolbox based on MATLAB is used for simulation verification and joint space trajectory planning simulation.

Optimization Control of Cooperative Trajectory towards Dual Arms Based on Time-Varying Constrained Output State

Aiming at the impact and disturbance of dual-arm robots in the process of coordinated transportation, a dual-arm cooperative trajectory optimization control based on time-varying constrained output state is proposed. According to the constraint relationship of the end-effector trajectory of the dual-arm coordinated transportation, the joint space trajectory mathematical model of the dual-arm coordinated transportation was established by using the master-slave construction method. Based on the time impact optimization index of joint trajectory, a multiobjective nonlinear equation is established. Using random probability distribution to extract the interpolation features of nonuniform quintic B-spline trajectory, the feature optimization target is selected, and the Newton numerical algorithm is used for iterative optimization. At the same time, it is combined with an elite retention genetic algorithm to further optimize the target. Based on the disturbance and tracking problem, a PD control method based on time-varying constrained output state is proposed, and the control law is designed. Its convergence is verified by establishing the Lyapunov function equation and asymmetric term. The trajectory optimization results show that the proposed trajectory optimization method can increase the individual diversity and enhance the individual local optimization, thus avoiding the premature impact of the elite retention genetic algorithm. Finally, the proposed control method is simulated on the platform of Gazebo; compared with the traditional PD control method, the results show that the proposed control algorithm has high robustness, and the rationality of the coordinated trajectory control method is verified by the double-arm handling experiment.

Robust control of uncertain robotic systems: An adaptive friction compensation approach

This paper solves the robust control problem of robotic manipulator systems with uncertain dynamics by friction compensation approach. A weighting factor is introduced to distinguish the role of friction in control process by comparing the directions of sliding vector and friction. Utilizing the weighting factor, model-based and model-free adaptive friction compensation controllers are designed to achieve asymptotical tracking of the desired joint-space trajectory according to the knowledge of friction. The damping property of friction is fully used to improve the control performance by compensating the friction harmful for the stability, and on the other hand, utilizing the beneficial friction. Numerical simulations are given to demonstrate the control performance of the proposed approach.

A probabilistic framework for learning geometry-based robot manipulation skills

Programming robots to perform complex manipulation tasks is difficult because many tasks require sophisticated controllers that may rely on data such as manipulability ellipsoids, stiffness/damping and inertia matrices. Such data are naturally represented as Symmetric Positive Definite (SPD) matrices to capture specific geometric characteristics of the data, which increases the complexity of hard-coding them. To alleviate this difficulty, the Learning from Demonstration (LfD) paradigm can be used in order to learn robot manipulation skills with specific geometric constraints encapsulated in SPD matrices.Learned skills often need to be adapted when they are applied to new situations. While existing techniques can adapt Cartesian and joint space trajectories described by various desired points, the adaptation of motion skills encapsulated in SPD matrices remains an open problem. In this paper, we introduce a new LfD framework that can learn robot manipulation skills encapsulated in SPD matrices from expert demonstrations and adapt them to new situations defined by new start-, via- and end-matrices. The proposed approach leverages Kernelized Movement Primitives (KMPs) to generate SPD-based robot manipulation skills that smoothly adapt the demonstrations to conform to new constraints. We validate the proposed framework using a couple of simulations in addition to a real experiment scenario.

Fractional-order iterative learning control for robotic Arm-PD2Dα type

In this paper, a new open-loop PD2D? type a fractional order iterative learning control (ILC) is studied for joint space trajectory tracking control of a linearized uncertain robotic arm. The robust convergent analysis of the tracking errors has been done in time domain where it is theoretically proven that the boundednesses of the tracking error are guaranteed in the presence of model uncertainty. The convergence of the proposed open-loop ILC law is proven mathematically using Gronwall integral inequality for a linearized robotic system and sufficient conditions for convergence and robustness are obtained.

Robot arm trajectory planning study for a table tennis robot

The 4 degree of freedom robot arm of a table tennis robot has a variety of trajectories. In order to improve the response and the success rate of the shots, we used the joint space trajectory planning method to establish a kinematic model with the robot arm joints as variables, and by combining it with the robot arm kinematics, we obtained the relevant parameters for each joint of the robot arm. Simulation tests and physical tests were carried out to obtain a more accurate trajectory of the robot arm.

Tuning Proportional-Integral-Derivative Gains of a Three-Dimensional RRRP Pick and Place Robot for Asymptotic Trajectory Tracking

Abstract This paper uses the Floquet theory for tuning the feedback gains to stabilize the tracking errors of a revolute-revolute-revolute-prismatic (RRRP) robot moving in a three-dimensional (3D) workspace. This robot is driven by a proportional-integral-derivative (PID) control law, tracking a time-varying trajectory in joint space, without knowledge of any bounds of the inertia matrix and/or Jacobian of the gravity vector. The Floquet theory is used to obtain the values of feedback gains for which the asymptotic stability of the tracking errors is obtained. The numerical results obtained by Floquet theory are verified by the tracking error plots and phase portraits. The obtained results will be very useful for the control of any industrial robot, required to perform repetitive tasks like assembly of parts and inspection of products, amongst others.

A New Adaptive RISE Feedforward Approach based on Associative Memory Neural Networks for the Control of PKMs

In this paper, a RISE (Robust Integral of the Sign Error) controller with adaptive feedforward compensation terms based on Associative Memory Neural Network (AMNN) type B-Spline is proposed to regulate the positioning of a Delta Parallel Robot (DPR) with three degrees of freedom. Parallel Kinematic Manipulators (PKMs) are highly nonlinear systems, so the design of a suitable control scheme represents a significant challenge given that these kinds of systems are continually dealing with parametric and non-parametric uncertainties and external disturbances. The main contribution of this work is the design of an adaptive feedforward compensation term using B-Spline Neural Networks (BSNNs). They make an on-line approximation of the DPR dynamics and integrates it into the control loop. The BSNNs’ functions are bounded according to the extreme values of the desired joint space trajectories that are the BSNNs’ inputs, and their weights are on-line adjusted by gradient descend rules. In order to evaluate the effectiveness of the proposed control scheme with respect to the standard RISE controller, numerical simulations for different case studies under different scenarios were performed.

Fuzzy neural network control for mechanical arm based on adaptive friction compensation

When tracking the trajectory of the mechanical arm in a joint space, the system is affected by friction non-linearity, unknown dynamic parameters and external disturbances that makes it difficult to improve the control accuracy of the mechanical arm. To solve the above problems, this paper introduces LuGre friction model and designs a new joint space trajectory tracking controller based on the adaptive fuzzy neural network. The controller is capable to make the adaptive adjustment of the center and width of the basis function, can approach the nonlinear link having the LuGre friction on line, and uses the sliding mode control term to reduce the approximation error. The introduction of LuGre model into the mechanical arm system can more truly simulate the friction link of the system, which is of great significance to the high precision control of the mechanical arm. The Lyapunov method is used to prove the stability of the closed-loop system. The simulation results show that the designed adaptive fuzzy neural network can effectively compensate the non-linear links including friction without precise system parameters, and the controller has strong robustness to load changes, thus realizing high-precision trajectory tracking of the mechanical arm in joint space.

Inverse Kinematics of Redundant Manipulators With Dynamic Bounds on Joint Movements

Redundant manipulators are usually required to perform tasks in the operational space, but collision-free path planning is computed in the configuration space. Limiting the deviation with respect to the collision-free configuration-space trajectory may allow the robot to avoid collisions without modifying the primary task. This letter proposes a method to guarantee that the solution of the inverse kinematic problem deviates from the nominal joint-space trajectory less than a desired threshold. The excursion limitation is ensured by means of linear constraints and the automatic regulation of the weights of secondary tasks. Numerical and experimental results prove the validness of the proposed approach.

Analysis and Optimization of Interpolation Points for Quadruped Robots Joint Trajectory

Trajectory planning is the foundation of locomotion control for quadruped robots. This paper proposes a bionic foot-end trajectory which can adapt to many kinds of terrains and gaits based on the idea of trajectory planning combining Cartesian space with joint space. Trajectory points are picked for inverse kinematics solution, and then quintic polynomials are used to plan joint space trajectories. In order to ensure that the foot-end trajectory generated by the joint trajectory planning is closer to the original Cartesian trajectory, the distributions of the interpolation point are analyzed from the spatial domain to temporal domain. An evaluation function was established to assess the closeness degree between the actual trajectory and the original curve. Subsequently, the particle swarm optimization (PSO) algorithm and genetic algorithm (GA) for the points selection are used to obtain a more precise trajectory. Simulation and physical prototype experiments were included to support the correctness and effectiveness of the algorithms and the conclusions.

A Multi-Objective Trajectory Planning Method for Collaborative Robot

Aiming at the characteristics of high efficiency and smoothness in the motion process of collaborative robot, a multi-objective trajectory planning method is proposed. Firstly, the kinematics model of the collaborative robot is established, and the trajectory in the workspace is converted into joint space trajectory using inverse kinematics method. Secondly, seven-order B-spline functions are used to construct joint trajectory sequences to ensure the continuous position, velocity, acceleration and jerk of each joint. Then, the trajectory competitive multi-objective particle swarm optimization (TCMOPSO) algorithm is proposed to search the Pareto optimal solutions set of the robot’s time-energy-jerk optimal trajectory. Further, the normalized weight function is proposed to select the appropriate solution. Finally, the algorithm simulation experiment is completed in MATLAB, and the robot control experiment is completed using the Robot Operating System (ROS). The experimental results show that the method can achieve effective multi-objective optimization, the appropriate optimal trajectory can be obtained according to the actual requirements, and the collaborative robot is actually operating well.

Model-predictive reference trajectory planning for redundant pneumatic collaborative robots

Abstract Collaborative robots have the potential to simplify the working day of the future. The goal in the development of these robots is to assist human operators by handling all sorts of tasks. A common underlying problem is to move the robot’s tool center point in a desired way. In this work we consider the generation of a feasible trajectory in joint space given a reference in task space. This is done at the example of the Bionic Handling Assistant (BHA), a compliant, redundant and pneumatically driven continuum robot. The trajectory for the BHA is obtained using a model control loop (MCL) which internally realizes a nonlinear model predictive controller (NMPC). We simplify the high dimensional and nonlinear model of the BHA to a computational efficient model which still covers the major effects of the original dynamics. This results not only in a feasible trajectory but also enables the model control loop to be real-time applicable. The proposed method is validated in simulation.

Object-Centric Task and Motion Planning in Dynamic Environments

We address the problem of applying Task and Motion Planning (TAMP) in real world environments. TAMP combines symbolic and geometric reasoning to produce sequential manipulation plans, typically specified as joint-space trajectories, which are valid only as long as the environment is static and perception and control are highly accurate. In case of any changes in the environment, slow re-planning is required. We propose a TAMP algorithm that optimizes over Cartesian frames defined relative to target objects. The resulting plan then remains valid even if the objects are moving and can be executed by reactive controllers that adapt to these changes in real time. We apply our TAMP framework to a torque-controlled robot in a pick and place setting and demonstrate its ability to adapt to changing environments, inaccurate perception, and imprecise control, both in simulation and the real world.

DPSO and Inverse Jacobian-Based Real-Time Inverse Kinematics With Trajectory Tracking Using Integral SMC for Teleoperation

A six-degree-of-freedom robotic manipulator inverse kinematics (IK) for position control is proposed for the bilateral teleoperation process that is implemented through a joystick for nuclear power plant dismantling operations. The control strategy of the manipulator includes the use of the joystick to generate the Cartesian space trajectory followed by the IK to yield the joint space trajectory for implementing position control. In this paper, a novel technique for the IK is proposed. It involves the use of the particle swarm optimization (PSO) algorithm with the inverse Jacobian (IJ). The special case of the dual PSO is based on dividing the PSO algorithm into two such that the trajectory position and orientation are separately optimized by the algorithms, resulting in a faster convergence. In contrast, the inverse Jacobian aids in generating a smooth joint trajectory. The integral sliding mode control (ISMC) is proposed for position control because it does not require information on system dynamics. The ISMC improves the system trajectory tracking performance by using a switching gain to compensate for system dynamics and perturbations (disturbance and unmatched uncertainties), ultimately reducing the time delay. The effectiveness of the PSO combined with the IJ and the robustness of the ISMC in the teleoperation process are confirmed by the experimental results.