Joint Space Trajectory Research Articles

Trajectory Planning for Reconfigurable Industrial Robots Designed to Operate in a High Precision Manufacturing Industry

This paper presents an algorithm for an automated planning of time-jerk optimal trajectories on a reconfigurable robot with an anthropomorphic structure. The trajectory planning algorithm is designed to provide reachable input set-points for the reconfigurable control system to accommodate not only changes in task objectives but also various reconfigurations of the robot kinematic structure and motion behavior adaptation in response to operational constraints. Firstly, appropriate reference frames are defined on the robotic modules and the position and orientation of the end effector in the Cartesian space is dynamically generated through a reconfigurable forward kinematics module. Secondly, through an iterative inverse kinematic method, the robot configuration space for the start and goal destinations and the geometric path for every motion tasks are generated. Finally, the joint space trajectories with coordinated motion profiles are generated by incorporating the motion laws and joint kinematic parameter values. The general outcome of the algorithm is a trajectory plan of the robot joints expressed as a time history of the robot motion. The trajectories are dynamically generated to satisfy widely varying tasks, constraints and objectives aiming towards a fully reconfigurable control without any hardware or software adjustment.

Learning Trajectories for Robot Programing by Demonstration Using a Coordinated Mixture of Factor Analyzers.

This paper presents an approach for learning robust models of humanoid robot trajectories from demonstration. In this formulation, a model of the joint space trajectory is represented as a sequence of motion primitives where a nonlinear dynamical system is learned by constructing a hidden Markov model (HMM) predicting the probability of residing in each motion primitive. With a coordinated mixture of factor analyzers as the emission probability density of the HMM, we are able to synthesize motion from a dynamic system acting along a manifold shared by both demonstrator and robot. This provides significant advantages in model complexity for kinematically redundant robots and can reduce the number of corresponding observations required for further learning. A stability analysis shows that the system is robust to deviations from the expected trajectory as well as transitional motion between manifolds. This approach is demonstrated experimentally by recording human motion with inertial sensors, learning a motion primitive model and correspondence map between the human and robot, and synthesizing motion from the manifold to control a 19 degree-of-freedom humanoid robot.

Practical high curvature path planning algorithm in joint space

A practical high curvature path planning algorithm that considers the velocity limit of a mobile robot in joint space is proposed. The existence of obstacles that constrict the smooth movement of mobile robots is inevitable. To avoid incoming collision, the robot is redirected to a new path with respect to the dimensions of the obstacle and a safety factor. The redirected path consists of geometric constraints such as high curvatures on its turning points which cause difficulty in controlling the mobile robot. Thus, a central velocity generation method that considers both velocity limits through a convolution operator and high curvatures at turning points is suggested. The central velocity is able to be within the configured velocity limit, otherwise actual velocity commands in joint space could result. Therefore, interpolation to obtain uniform sampling and velocity downscaling is performed to generate a feasible joint space trajectory. The result shows short travelling time compared with previous methods while satisfying velocity limits in the joint space.

Integrated Trajectory Planning and Sloshing Suppression for Three-Dimensional Motion of Liquid Container Transfer Robot Arm

For liquid transfer system in three-dimensional space, the use of multijoint robot arm provides much flexibility. To realize quick point-to-point motion with minimal sloshing in such system, we propose an integrated framework of trajectory planning and sloshing suppression. The robot motion is decomposed into translational motion of the robot wrist and rotational motion of the robot hand to ensure the upright orientation of the liquid container. The trajectory planning for the translational motion is based on cubic spline optimization with free via points that produces smooth trajectory in joint space while it still allows obstacle avoidance in task space. Input shaping technique is applied in the task space to suppress the motion induced sloshing, which is modeled as spherical pendulum with moving support. It has been found through simulations and experiments that the proposed approach is effective in generating quick motion with low amount of sloshing.

Implementation of Joint Space Trajectory Planning for Mobile Robots with Considering Velocity Constraints on Xenomai

This paper presents an implementation of trajectory planning method while considering velocity constraints for a two-wheeled mobile robot (TMR) on Xenomai. A Bezier curve is utilized to make a smooth path. A convolution operator was used to generate a velocity profile for the travel distance of the planned path while also giving consideration of the velocity constraints of the TMR. The trajectory planning are performed on Xenomai with multitasking structure, which is a real-time Linux system developed by open-source projects. Finally, the periodicity and schedulability of real-time tasks and trajectory tracking performance were analyzed. Moreover, the efficiency of real-time operating system was also examined.

A New Method of 6-DOF Serial Robot’s Trajectory Planning under Multi-Constraints

This paper proposes a new method of 6-DOF serial robot’s trajectory planning. Ensuring to satisfy the physical constraints of space conditions, the robot’s trajectory is interpolated in the Cartesian coordinate system, and using quaternion interpolation to solve the multiple solution problem in RPY interpolation. Meanwhile, the interpolated position information is transformed into the angular displacement information of the joint coordinate system, and the joint space trajectory planning is achieved using the genetic algorithms integrated velocity, acceleration, jerk and torque and other important kinematic and dynamic constraints. In robot safety and stability, the method is better than the general approach, and it has both the ideal trajectory parameters of the global search ability and performance planning.

Indirect robot model learning for tracking control

Learning task-space tracking control on redundant robot manipulators is an important but difficult problem. A main difficulty is the non-uniqueness of the solution: a task-space trajectory has multiple joint-space trajectories associated, therefore averaging over non-convex solution space needs to be done if treated as a regression problem. A second class of difficulties arise for those robots when the physical model is either too complex or even not available. In this situation machine learning methods may be a suitable alternative to classical approaches. We propose a learning framework for tracking control that is applicable for underactuated or non-rigid robots where an analytical physical model of the robot is unavailable. The proposed framework builds on the insight that tracking problems are well defined in the joint task- and joint-space coordinates and consequently predictions can be obtained via local optimization. Physical experiments show that state-of-the art accuracy can be achieved in both online and offline tracking control learning. Furthermore, we show that the presented method is capable of controlling underactuated robot architectures as well.

An Analytical Approach to Operational Space Control of Robotic Manipulators with Kinematic Constraints

This paper presents a novel control architecture for operational space control when the end effector or the robotic chain is kinematically constrained. Particularly, we address kinematic control of robots operating in the presence of obstacles such as point, plane, or barrier constraints imposed on a point on the manipulator. The main advantage of the proposed approach is that we are able to control the end-effector motion in the normal way using conventional operational space control schemes, and by re-writing the Jacobian matrix we also guarantee that the constraints are satisfied. The most challenging problem of obstacle avoidance of robotic manipulators is the extremely complex structure that arises when the obstacles are mapped from the operational space to joint space. We solve this by first finding a new set of velocity variables for a point on the robot in the vicinity of the obstacle, and on these new variables we impose a structure which guarantees that the robot does not hit the obstacle. We then find a mapping denoted the Constrained Jacobian Matrix from the joint variables to these new velocity variables and use this mapping to find a trajectory in joint space for which the constraints are not violated. We present for the first time the Constrained Jacobian Matrix which imposes a kinematic constraint on the manipulator chain and show the efficiency of the approach through experiments on a real robot.

Smooth Trajectory Planning for 3-UPU Parallel Manipulator

Exciting the mechanical resonance mode and vibration caused by non-smooth trajectories can cause some failure in the structure of the robot and its actuators. This work proposes a smooth trajectory planning for 3 degree of freedom (dof) 3-upu parallel manipulator. We have used optimization method to define the smooth trajectory for this robot. In this paper an objective function has been used which contain a term related to the total execution time and a term corresponding to the integral of squared jerk. Some constraints have been applied to the problem as the input of our system. Task space and joint space trajectory are then considered as the output. In this method optimization techniques such as genetic algorithm and fmincon (function of MatLabTM ) have been investigated. Six via points have been considered and B-splines have been used to present kinematic quantities.

Joint Space Trajectory Planning Considering Physical Limits with Convolution Operator for Mobile Robots

Joint Space Trajectory Planning Considering Physical Limits with Convolution Operator for Mobile Robots

FPGA based hardware accelerator for parallel robot kinematic calculations

The paper presents an application of FPGA to support the calculation of the inverse kinematics problem of a parallel robot. The presented robot is designed for milling by moving the spindle along a desired trajectory generated in Cartesian space. This means that for each point of the trajectory solution of the inverse kinematics problem is needed. The resulting sequence of data creates the joint space trajectory. The trajectory in joint space must be calculated in real time. Required high frequency and complex equations makes the problem of the calculation time crucial. The paper shows how to increase the computing power for inverse kinematics problem solving, preserving required calculation accuracy, by augmenting the arithmetic coprocessor with custom instructions. The paper shows hardware implementation of the accelerator and presents results of calculations per-formed on Altera FPGA chip.

Simplified Robotics Joint-Space Trajectory Generation with a via Point Using a Single Polynomial

This paper presents novel fourth- and sixth-order polynomials to solve the problem of joint-space trajectory generation with a via point. These new polynomials use a single-polynomial function rather than two-polynomial functions matched at the via point as in previous methods. The problem of infinite spikes in jerk is also addressed.

Design of a Servo Controller for Modularized Flexible Joint with Integrated Torque Sensors Based on SOPC

In this paper, a design of modularized flexible joint servo controller on-chip for a space manipulator system is presented. First of all, the structure and sensor system of dual-joint is introduced. The structural optimization design of the joint torque sensor is carried out with the help of the ANSYS program for weight minimization. Next, the features of the hardware system for the dual-joint controller are described. All sensor information collection within the joints are obtained with FPGA hardware logic elements using System-on-a-Programmable-Chip technology, and the joint space trajectory planning and position control are realized by Nios II soft-core processor, which is embedded in FPGA. Finally, experimental results demonstrate the effectiveness of the compact joint servo controller for the space manipulator system.

Application of GRNN to Plan Trajectory for a Picking Robot

In order to supply reference inputs for the robot system, a high-order polynomial function is proposed according to particular strategies to plan trajectory in joint space, which could provide continuous velocity, acceleration and jerk to ensure safety for electric actuators and stability of the robot during the motion process. The general regression neural network (GRNN) is constructed to realize the proposed polynomial function for its powerful non-linear mapping ability. Parameters of the spreading factor and number of training samples which influence the performances of the network are detailed analyzed. Simulation results show that GRNN has advantages of favorable stability and high precision of function approaching even with few samples. Finally, the trajectory planner based on GRNN is successfully applied for an articulated picking robot to realize the real-time control.

Cosine Second Order Robot Trajectory Planning Method

A new joint space trajectory planning method for the series robot is proposed. Comparing with the traditional path planning methods which can only guarantee the planned trajectory velocity or acceleration continuous, the proposed trajectory planning algorithm can also ensure the derivative of acceleration (Jerk) continuous within a limit threshold. At the end of this paper, the proposed path planning algorithm is validated of having a great performance on robot trajectory tracking.

Joint-space Trajectory Planning for Robots under Multiple Constraints

In the cases that the robots move fast with fixed motion time,various constraints,such as angular acceleration constraint,angular velocity constraint and angular constraint,should be considered when planning the trajectories of robots due to the driver performances and other factors.By analyzing the constraints,a joint-space trajectory planning method for robots under multiple constraints is proposed based on trapezoidal velocity profile.According to the minimum acceleration trajectory without constraints,the minimum acceleration trajectory under the angular velocity constraint and angular constraint is obtained by optimizing the angular acceleration while it is in the constraint range.The situation that the trajectory with maximum acceleration cannot meet the constraint requirements is discussed.The trajectory planning method takes into account both the moving stability and the constraints and can give full joint driving performances.Simulation results show the feasibility of the method.

Numerical issues in integrating holonomic kinematic inversion algorithms for redundant manipulators

Redundant robotic manipulators under kinematic control may exhibit unpredictable behaviours at joint level, since closed loop trajectories in Cartesian space do not in general map in closed loop trajectories in joint space. Holonomic kinematic inversion algorithms avoid this problem. In this paper, we point out some numerical problems that may arise when discretizing a holonomic kinematic inversion algorithm. It is shown that the knowledge of the additional set of holonomic constraints is needed in order to overcome such drawbacks. A simple case study that shows the potential effects of discretization is discussed.

Design and validation of an FPGA-based self-healing controller for hybrid machine tools

It has been recognised that the ability of dynamic reconfiguration and parallel computation for field programmable gate array (FPGA) provides significant advantages, particularly for increasing reliability and maintainability of electromechanical products. An FPGA-based self-healing controller for hybrid machine tools (HMTs) is developed to meet the high speed sampling rate requirement and a circuit of self-healing controllers as well as velocity profile generators for HMTs is designed using the very high speed integrated circuit hardware description language (VHDL) and implemented with an FPGA. A self-healing controller framework for HMTs is proposed and incorrectly measured leg position faults (LPFs) and incorrectly measured leg velocity faults (LVFs) are considered as examples. Faults are detected by fault detection and isolation (FDI) module considering the closed-loop kinematic chain constraints of spatial hybrid mechanism utilising a sensored passive leg. When a fault is detected, the control system and the desired joint space trajectory are reconfigured according to the nature of the isolated fault and the task is resumed to the largest extent possibility. Feasibility and performance of above self-healing controller are validated by experiments and simulation examples.

CARTESIAN APPROACH FOR GAIT PLANNING AND CONTROL OF BIPED ROBOTS ON IRREGULAR SURFACES

Biped robots possess higher capabilities than other mobile robots for moving on uneven environments. However, due to natural postural instability of these robots, their motion planning and control become a more important and challenging task. This article presents a Cartesian approach for gait planning and control of biped robots without the need to use the inverse kinematics and the joint space trajectories, thus the proposed approach could substantially reduce the processing time in both simulation studies and online implementations. It is based on constraining four main points of the robot in Cartesian space. This approach exploits the concept of Transpose Jacobian control as a virtual spring and damper between each of these points and the corresponding desired trajectory, which leads to overcome the redundancy problem. These four points include the tip of right and left foot, the hip joint, and the total center of mass (CM). Furthermore, in controlling biped robots based on desired trajectories in the task space, the system may track the desired trajectory while the knee is broken. This problem is solved here using a PD controller which will be called the Knee Stopper. Similarly, another PD controller is proposed as the Trunk Stopper to limit the trunk motion. Obtained simulation results show that the proposed Cartesian approach can be successfully used in tracking desired trajectories on various surfaces with lower computational effort.

Fuzzy Adaptive Compensator Control for Free-floating Space Manipulator With Unknown Payload Parameters to Track Desired Trajectory in Joint Space

讨论了载体姿态受控、位置不受控制情况下, 漂浮基空间机械臂载体姿态及机械臂 关节协调运动的控制问题. 利用拉格朗日方法并结合系统动量守恒关系, 建立了漂浮基空间机械臂完全能控形式的系统动力学方程. 以此为基础, 针对空间机械臂末 端爪手所持载荷参数未知的情况, 设计了一种基于标称计算力矩控制器附加模糊自适应补偿控制器的复合控制方案, 即通过模糊自适应补偿控制器来弥补系统未知参数对标称计算力矩控制器的影响, 以确保存在未知系统参数情况下整个闭环控制系 统的渐近稳定性. 文中提到的控制方案能够有效地控制漂浮基空间机械臂的载体姿态及机械臂关节, 可以协调地完成期望的轨迹运动, 并具有不需要反馈和测量空间机械臂载体 的位置、移动速度、移动加速度, 同时也不要求系统动力学方程关于系统惯性参数呈线性函数关系的显著优点. 通过系统数值仿真证实了方法的有效性.