Trapezoidal Velocity Profile Research Articles

FPGA implementation of higher degree polynomial acceleration profiles for peak jerk reduction in servomotors

Acceleration profile generation for jerk limitation is a major issue in automated industrial applications like computer numerical control (CNC) machinery and robotics. The automation machinery dynamics should be kept as smooth as possible with suitable controllers where trajectory precision ensures quality while smoothness decreases machinery stress. During the operation of commercially available CNC and robotics controllers, small discontinuities on the dynamics are generated due to the controller position profiler which is generally based on a trapezoidal velocity profile. These discontinuities can produce undesirable high-frequency harmonics on the position reference which consequentially can excite the natural frequencies of the mechanical structure and servomotors. Previous works have developed jerk limited trajectories with higher degree polynomial-based profiles, but lack one or both of computer efficiency for on-line operation and low-cost hardware implementation. The present work shows a low cost, computationally efficient, on-line hardware implementation of a high-degree polynomial-based profile generator with limited jerk dynamics for CNC machines and robotics applications to improve the machining process. The novelty of the paper is the development of a multiplier-free recursive algorithm for computationally efficient polynomial evaluation in profile generation and a low-cost implementation of the digital structure in field programmable gate array (FPGA). Two experimental setups were prepared in order to test the polynomial profile generator: the first one with the servomotor at no load and the second one for the servomotor driving a CNC milling machine axis. From experimental results it is shown that higher degree polynomial profiles, compared to the standard trapezoidal speed profile improve the system dynamics by reducing peak jerk in more than one order of magnitude while precision is maintained the same and on-line operation is guaranteed.

Ropeless Elevator With Linear Switched Reluctance Motor Drive Actuation Systems

Linear switched reluctance motor (LSRM) drives are investigated and proved in this study as an alternative actuator for vertical linear transportation applications such as a linear elevator. A one-tenth-scaled prototype elevator that is focused on a home elevator with LSRMs is designed, and extensive experimental correlation is presented for the first time in this paper. The proposed LSRM has twin stators and a set of translator poles without yoke placed between the two stators. The features of the LSRM and the prototype elevator are described. Furthermore, a control strategy for the prototype elevator is introduced consisting of four control loops, viz., (1) current, (2) force, (3) velocity, and (4) position feedback control loops. Force control of the experimental prototype elevator employs the proposed force distribution function. A trapezoidal velocity profile is introduced to control vertical travel position smoothly during ascent, descent, and stop of the elevator. Conventional proportional-integral controller is used for the current and velocity control loops and their designs are described. The proposed control strategy is dynamically simulated and experimentally correlated. The analytical and experimental results of this paper prove that LSRMs are one of the strong candidates for linear elevator propulsion drives.

3325 マルチセグメント・スライディングモード法によるクーロン摩擦を有するボールネジ駆動装置の位置決め制御(非線形制御理論とその応用(2))

This paper deals with a positioning control of a ball-screw driven system. The objective is to control the motion specified by a trapezoidal velocity profile and to achieve the highly accurate positioning, using multi-segment sliding mode control method. The multi-segment switching functions are designed to satisfy the state trajectories corresponding to the trapezoidal velocity profile. The proposed control method is applied to the system driven by an AC servomotor to verify its control performances. The experimental results show that the proposed technique is applicable to the acceleration and deceleration motion even in the range of 2gm/s^2 (g is the gravitational acceleration) and effectively suppresses a position error as well as an overshoot in comparison with the conventional PID control techniques.

A universal velocity profile generation approach for high-speed machining of small line segments with look-ahead

Usually a complex contour-machining program generated by CAD/CAM systems composes a lot of small line segments. The intelligence of look-ahead is key to meeting the demand of high speed and high accuracy in the machining of these line segments. By now most researchers just utilize the simplest trapezoidal velocity profiles to deal with the look-ahead problem. Also the number of look-ahead line segments in most commercially available CNC systems is fixed, which cannot make full use of CNC processors. Therefore, a universal velocity profiles generation approach and corresponding optimal look-ahead algorithm based on dynamic back tracking along a doubly linked list are proposed in this paper. Two novel strategies, one for reducing feed rates fluctuation and the other for reducing move errors that come from digital integration and accumulated computation, are also presented. By using the proposed look-ahead techniques, arbitrary velocity profiles having the desired acceleration and deceleration characteristics for the movement of a lot of small line segments can be generated efficiently. Thus, the machining productivity can be dramatically increased without sacrifice of accuracy. The results of simulations and experiments showed the proposed approach was feasible and effective.

Application of a Perturbation Method for Realistic Dynamic Simulation of Industrial Robots

This paper presents the application of a perturbation method for the closed-loop dynamic simulation of a rigid-link manipulator with joint friction. In this method the perturbed motion of the manipulator is modelled as a first-order perturbation of the nominal manipulator motion. A non-linear finite element method is used to formulate the dynamic equations of the manipulator mechanism. In a closed-loop simulation the driving torques are generated by the control system. Friction torques at the actuator joints are introduced at the stage of perturbed dynamics. For a mathematical model of the friction torques we implemented the LuGre friction model that accounts both for the sliding and pre-sliding regime. To illustrate the method, the motion of a six-axes industrial Staubli robot is simulated. The manipulation task implies transferring a laser spot along a straight line with a trapezoidal velocity profile. The computed trajectory tracking errors are compared with measured values, where in both cases the tip position is computed from the joint angles using a nominal kinematic robot model. It is found that a closed-loop simulation using a non-linear finite element model of this robot is very time-consuming due to the small time step of the discrete controller. Using the perturbation method with the linearised model a substantial reduction of the computer time is achieved without loss of accuracy.

A Novel Motor Drive Design for Incremental Motion System via Sliding-Mode Control Method

This paper proposes a particular motor position control drive design via a novel sliding-mode controller. The newly designed controller is especially suitable for the motor incremental motion control which is specified by a trapezoidal velocity profile. The novel sliding-mode controller is designed in accordance with the trapezoidal velocity profile to guarantee the desired performance. A motor control system associated PC-based incremental motion controller with permanent-magnet synchronous motor is built to verify the control effect. The validity of the novel incremental motion controller with sliding-mode control method is demonstrated by simulation and experimental results.

JERK LIMITED VELOCITY PROFILE GENERATION FOR HIGH SPEED INDUSTRIAL ROBOT TRAJECTORIES

Trapezoidal velocity profiles are no longer sufficient for recent high speed industrial robots involved in precision works. Most of the recently developed trajectory generation algorithms have adopted jerk limited profiles, where computation of the coefficients is intricate. The previous algorithms have attempted either to obtain suboptimal solutions or to solve the problem in an iterative manner which complicates on-line implementation. This paper presents analytic solutions to the computational problem. The solutions presented are derived from the simultaneous equations for displacement condition and peak velocity condition, where jerk, acceleration and velocity constraints are resolved. By including only the low-order polynomial equations that can be evaluated analytically, the proposed algorithm is readily implementable on the fly.

3920 マルチセグメント・スライディングモードコントローラによる駆動装置の速度制御(G10-4 制振,免振,振動低減(2),G10 機械力学・計測制御)

This paper deals with a motion control problem of a uni-axial ball-screw slide system driven by an AC servomotor. The objective is to control the motion specified by the trapezoidal velocity profile, using the multi-segment sliding mode control method. The method that has been originally proposed by Shyu et al is modified and used in the present study to simplify the control law and to alleviate the chattering phenomenon. The validity of the control law is examined by the numerical simulations and the experiments.

JOINT SPACE POINT-TO-POINT MOTION PLANNING FOR ROBOTS. AN INDUSTRIAL IMPLEMENTATION

A path-following algorithm for industrial robots is presented in this paper. The algorithm generates off-line a joint space point-to-point trajectory that, by exploiting knowledge of the dynamic model, takes into account the actuators’ torque limits while preserving the geometric path. Due to the software characteristic of the specific industrial architecture, the trajectories adopt a trapezoidal velocity profile. The algorithm has been designed, implemented and extensively tested on a Comau SMART H4 robot, a closed-chain six-degree-of-freedom industrial manipulator.

Incremental motion control of linear synchronous motor

In this study a particular incremental motion control problem, which is specified by the trapezoidal velocity profile using multisegment sliding mode control (MSSMC), is proposed to control a permanent magnet linear synchronous motor (PMLSM) servo drive system. First, the structure and operating principle of the PMLSM are described in detail. Second, a field-oriented control PMLSM servo drive is introduced. Then, each segment of the multisegment switching surfaces is designed to match the corresponding part of the trapezoidal velocity profile, thus the motor dynamics on the specified-segment switching surface have the desired velocity or acceleration corresponding part of the trapezoidal velocity profile. In addition, the proposed control system is implemented in a PC-based computer control system. Finally, the effectiveness of the proposed PMLSM servo drive system is demonstrated by some simulated and experimental results.

Incremental motion control of synchronous reluctance motor via multisegment sliding mode control method

This paper solves a particular incremental motion control problem, which is specified by the trapezoidal velocity profile, using multisegment sliding mode control. Each segment of the multisegment switching surfaces is designed to match the corresponding part of the trapezoidal velocity profile, so that the motor dynamics on the specified-segment switching surface have the desired velocity or acceleration corresponding to the trapezoidal profile. The multisegment sliding mode control is applied to a synchronous reluctance motor system to demonstrate its effectiveness. A PC-based prototype system is built to verify the validity of the proposed scheme.

Cartesian spline interpolation for industrial robots

We describe an algorithm for interpolation of positions by a rational spline motion. A reparameterization of the resulting motion is applied in order to achieve the desired distribution of the velocity. For the ease of presentation we discuss trapezoidal velocity profiles, i.e. piecewise constant and linear velocity distribution. The method can be generalized to more general velocity profiles. The whole spline scheme possesses some special features which make it a suitable tool for the control of industrial robots.

A control for a crank shear that minimizes the RMS current

A motor driving a crank sees a nonuniform load. Thus, it is difficult to determine a minimal-energy strategy for controlling the crank. The minimal energy problem is formulated and solved for boundary conditions appropriate to a crank shear. Since this exact solution is difficult to implement in a control system, an approximate solution, based on a symmetric-ramp torque profile, is also presented. It was confirmed by experiments that this near-optimum velocity profile yields considerable savings in RMS current over the standard trapezoidal velocity profile. >

Time optimization of the continuous-path motions of industrial robots

This paper presents an engineering approach to the time optimization of robotic motions with specified paths and trapezoidal velocity profiles. Optimizations of this type occur when dealing with continuous-path motions of commercial manipulators. Parameterized path equations and full non-linear robot dynamics are used in conjunction with the actuator limitations and the specified path and velocity profile in order to transform the problem into a non-linear programming form. The optimal velocity profile and the corresponding joint torques/forces are obtained via a simple search algorithm, without resorting to any constrained optimization technique, numerical integration, or search for the switching curve. Three examples of time-optimized robotic motions are presented.

Optimum trajectory for robot translational contouring under constraints imposed by joint motor capacities

A unique method has been developed to solve the optimal trajectory planning problem for a special robot application which can be characterized as: translational contouring with (1) a uniform cruising velocity along the desired path and (2) a trapezoidal velocity profile in each job segment. The method presented in the paper is based on the theoretical findings that for such an operation the joint velocities are directly proportional to the cruising velocity of the end-effector, and the joint accelerations are directly proportional to the square of the same cruising velocity. A computer simulation of a typical task is robot translational contouring was carried out to demonstrate the methodology. The results obtained have shown the efficiency and effectiveness of the method.

Vertical vestibuloocular reflex in cat: asymmetry and adaptation

1. We studied eye velocity during the first 2 s of the vertical vestibuloocular reflex (VOR) elicited from cats placed on their sides (90 degrees roll position) and rotated about an earth vertical axis. Vestibular stimuli were presented in the dark and consisted of brief trapezoidal velocity profiles. Eye movements were recorded with a magnetic search coil, and eye velocity was analyzed with high temporal resolution. 2. The first 2 s of upward or downward eye velocity after the onset of head rotation was characterized and compared. Adaptive changes in VOR gain (eye/head velocity) were then induced, and upward and downward eye velocity responses were again compared. 3. The early time course of the vertical VOR was complex. After a latency of approximately 15 ms, eye velocity increased rapidly until it was equal in magnitude and opposite in direction to head velocity. The peak eye velocity decayed within less than 1 s to a plateau of slow-phase eye velocity (SPEV) equal to approximately -0.6 times the head velocity. Peak upward and downward eye velocity was symmetric. The transition from peak to plateau was more rapid for the downward VOR (slow phases downward) than for the upward VOR (slow phases upward). The plateau attained by upward SPEV was approximately 15% higher than the plateau attained by downward SPEV. 4. VOR gain adaptation was symmetric. The percentage change in adapted upward eye velocity equalled the percentage change in adapted downward eye velocity. Both peak and plateau SPEV adapted, but peak eye velocity adapted less than plateau eye velocity. VOR latency was unchanged by adaptation. 5. The trajectory of the VOR response to steps of head velocity could be divided into an invariant and a variant interval. The invariant interval consisted of the initial approximately 15 ms of the eye movement. Neither direction of head movement (upward vs. downward) nor adaptation of the VOR gain effected the eye movement trajectory during the invariant interval. The variant interval began approximately 30 ms after the onset of head movement and approximately 15 ms after the onset of eye movement. In unadapted animals, downward eye speed exceeded upward eye speed during the variant interval. In adapted animals, eye speed during the variant interval, but not during the invariant interval, diverged from eye speed in the unadapted state. We suggest that the initial invariant interval (approximately 15 ms) of the eye movement response trajectory may represent the direct response of the classically described three-neuron arc.(ABSTRACT TRUNCATED AT 400 WORDS)

Influence of voluntary ocular deviation on vestibular nystagmus.

We examined the influence of voluntary gaze deviation on per-rotary vestibular nystagmus during trapezoidal velocity profiles. Gaze deviation in the direction of the fast-phase component of nystagmus significantly increased slow-phase amplitude, fast-phase amplitude and slow-phase velocity; gaze deviation in the direction of the slow phase marginally decreased these three properties. Schlagfeld deviation and beat frequency were unaffected by per-rotary ocular deviation in either direction. The observed changes in per-rotary eye movements are consistent with post-rotary observations first described by Alexander which later became known as "Alexander's Law".

Visual-vestibular convergence in the vestibular nuclei of the cat

Responses from neurons of the vestibular nuclei were recorded in N2O-anaesthetized cats. Most neurons in the rostral parts of the nuclei responded to bimodal visual-vestibular stimulation, following a trapezoidal velocity profile. Both combinations of the two stimuli were tested: rotation of the animal with stationary visual field and rotation with overtaking visual field, i.e. the visual pattern running in the same direction as the turntable with twice the velocity. Some correlation of physiological data with results in corresponding psychophysical experiments were found. As a possible biological function of visual-vestibular convergence a phylogenetic solution for discrimination of body and outer world movement is discussed.