Path planning and trajectory planning are crucial issues in the field of Robotics and, more generally, in the field of Automation. Indeed, the trend for robots and automatic machines is to operate at increasingly high speed, in order to achieve shorter production times. The high operating speed may hinder the accuracy and repeatability of the robot motion, since extreme performances are required from the actuators and the control system. Therefore, particular care should be put in generating a trajectory that could be executed at high speed, but at the same time harmless for the robot, in terms of avoiding excessive accelerations of the actuators and vibrations of the mechanical structure. Such a trajectory is defined as smooth. For such reasons, path planning and trajectory planning algorithms assume an increasing significance in robotics. Path planning algorithms generate a geometric path, from an initial to a final point, passing through pre-defined via-points, either in the joint space or in the operating space of the robot, while trajectory planning algorithms take a given geometric path and endow it with the time information. Trajectory planning algorithms are crucial in Robotics, because defining the times of passage at the via-points influences not only the kinematic properties of the motion, but also the dynamic ones. Namely, the inertial forces (and torques), to which the robot is subjected, depend on the accelerations along the trajectory, while the vibrations of its mechanical structure are basically determined by the values of the jerk (i.e. the derivative of the acceleration). Path planning algorithms are usually divided according to the methodologies used to generate the geometric path, namely:


roadmap techniques


cell decomposition algorithms


artificial potential methods.

Path Planning and Trajectory Planning Algorithms: A General Overview

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A key role of the CNC is to perform the feedrate interpolation which consists in generating the setpoints sent to each axis of a machine tool based on a NC program In high speed machining, the feedrate is limited by the velocity, acceleration and jerk of each axis of the machine tool The algorithm presented in this paper aims to obtain an optimized feedrate profile which makes best use of the kinematical characteristics of the machine This minimum time feedrate profile is computed by intersecting all the constraints due to the drives in an iterative algorithm It is worth noting that both tangential jerk and axis jerk are taken into consideration The proposed VPOp (Velocity Profile Optimization) method is universal and can be applied to any articulated mechanical structure as it is demonstrated in the examples Moreover the algorithm has been implemented for various formats: linear interpolation (G1) and NURBS interpolation in 3- and 5-axes The effectiveness of the algorithm is demonstrated thanks to a comparison with an industrial CNC and can be freely tested using the VPOp software which is available on the Internet http://webservlurpaens-cachanfr/geo3d/premium/vpop 

/pdf/feedrate-interpolation-with-axis-jerk-constraints-on-5-axis-52ejjhzc01.pdf

Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path

Active vibration control of a flexible beam using a non-collocated acceleration sensor and piezoelectric patch actuator

Conventional tool paths for computer numerical-controlled (CNC) machine tools or NC positioning systems are mainly composed of linear motion segments, or the so-called G1 commands. This approach exhibits serious limitations in terms of achieving the desired part of geometry and productivity in high-speed machining. Velocity and acceleration discontinuities occur at the junction points of consecutive segments. In order to generate smooth and continuous feed motion, a geometric corner smoothing algorithm is proposed in this paper, which fits quintic B-splines to blend adjacent straight lines together. The proposed transition scheme ensures G
 2 continuity transitions and optimal curvature geometry delivering fast cycle time without violating the axis acceleration limits. The cornering error is controlled analytically allowing the user to set the desired cornering tolerance. The feed profile along the corner-blended tool path is generated based on S-curve-type acceleration profile, and it is scheduled for minimum cycle time. At last, the corner-blended tool path is interpolated in real-time with minimum feed fluctuation for accurate and smooth feed motion. Proposed algorithms are implemented, and their effectiveness is tested on a CNC machine tool.

A curvature optimal sharp corner smoothing algorithm for high-speed feed motion generation of NC systems along linear tool paths

A controller using acceleration feedback has been applied to a flexible robot for which the position and velocity of the load are not measured. It is shown that acceleration feedback allows an exact tracking of the motor position, irrespective of the non-linear flexibilities of the axes and of the measurement disturbances. This easy-to-tune algorithm whose main control parameters are the modal masses of the motor and load part, and only consists of a positive acceleration feedback plus a PD controller, has been validated on an industrial robot with orthogonal axes.

Control of an Industrial Robot using Acceleration Feedback

The invention concerns a load handling device (7) to transfer and/or maintain the static state, this device consisting of at least one structure (9), an actuator (6) allowing the movement of the load (7) carried or transported by the structure (9) and at least once element (2) used to control the actuator (6) perceptible to the static movements of the structure (9), such as bending, vibrations, deformations of the structure (9), said static movements causing modifications of the control command (11) provided by the operator of the device (2) and the emission of a control signal inadvertently generated (3). This device is characterised in that it includes means (12) of detecting static movements of the structure (9) connected to the means (4) of handling inadvertently generated control signals (3) in order to limit or suppress all impact of said static movements in the inadvertently generated control signal (3) and to obtain a control signal (5) conforming to the control order (11) provided by the operator (1).

Load handling device

Resume Dans les machines-outils a grande vitesse, les trois parties : structure, mecanisme et commande sont fortement interdependantes. Il faut donc les modeliser pour maitriser l'incidence des pilotages des differents moteurs sur la situation du point a controler (broche ou piece selon le cas), en terme de precision et temps de reponse. Apres une introduction sur l'avenement des machines-outils agiles pour repondre aux besoins de l'automobile, ce papier fait le point sur la modelisation d'une machine-outil equipee de moteurs lineaires. Les performances globales d'une machine de production sont definies a partir de tous les constituants de la structure mecanique d'une part, et, d'autre part, de la strategie de commande adoptee pour rigidifier la liaison entre la consigne de reference et la position a maitriser. Un autre point important aborde concerne l'apport de nouvelles strategies d'asservissement pour faire face aux souplesses mecaniques et aux couplages entre les axes.

Modélisation du comportement dynamique et commande d'une machine-outil agile

A controller using acceleration feedback has been applied to a flexible robot for which the position and velocity of the load are not measured. It is shown by using the Causal Ordering Graph (COG), that the motor can be controlled by using acceleration feedback and that it allows an exact tracking of the motor position, irrespective of the non-linear flexibilities of the axis and of the measurement disturbances. This easy-to-tune algorithm, in which main control parameters are the modal masses of the motor and load part and only consists of a positive acceleration feedback plus a PD controller, has been validated on an industrial 3-axis robot.

Use of the cog representation to control a robot with acceleration feedback

robot. The focus of this paper is on the particular influence of the jerk limited profile on the dynamic behaviour of a 3-axis Cartesian robot. This robot is used for the unloading of the moulding machines. The predominating performances criteria are the movement time and the residual vibrations induced by high dynamical demands. The performances of a jerk limited movement law are evaluated using an analytical model of the controlled system. We show that the jerk lime parameter can be used to limit the residual vibrations while preserving the movement time by a combined action on the position loop gains. Experimental measurements demonstrate the effectiveness of the proposed approach.

/pdf/influence-du-jerk-sur-le-comportement-dynamique-d-un-robot-3rwzd04etn.pdf

Influence du jerk sur le comportement dynamique d'un robot cartésien 3 axes

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