Soft motion planning - Managing velocity, acceleration and jerk

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Fernando Figueiredo1 and Nelson Neves2 SMILE.TECH - ROBĂ“TICA, LDA / ISPGAYA – Instituto Superior PolitĂŠcnico Gaya 2 WIDESKILLS – Inovação, Projetos e Soluçþes, Lda. / ISPGAYA – Instituto Superior PolitĂŠcnico Gaya E-mail: @smlt.pt 1

robĂłtica

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artigo cientĂ­fico

Soft motion planning – Managing velocity, acceleration and jerk ABSTRACT The most basic feature of a robot is to be able to move, that motion should be controlled in a way that the required displacement is made in a required time, but also controlling velocity, acceleration (and therefore force) and comfort, (at least to the eye of the viewer). There are many possible strategies to deďŹ ne motion control laws, with more or less detail, the least controlled, just moves a cursor at a constant velocity, but we can also introduce an acceleration ramp, witch can be at a constant rate or can evolve at a rate called jerk. The most complex algorithms require more processing power but also allow greater dynamics with lower eort from drives and mechanics, and also greater comfort. We will describe the calculations required for an implementation that can be handled by a 32 bit microprocessor with math co-processor (ARM Cortex M3) in under 50ns, intended to give a good stability for robot manipulators with elastic transmission.

where tn is the time of each stage and etn is the elapsed time from the beginning of the movement to the end of each stage. The governing expressions for a, v and x are the following:

Keywords: soft motion, velocity, acceleration, jerk, s-curve

For the acceleration stages, we have:

INTRODUCTION In the development of a robot controller, the motion control routines are of crucial importance, more so when the robot’s structure and actuators are intended to have a not negligible elasticity. This article will describe the development, of the laws of motion and their implementation as an algorithm. Finally, we will demonstrate the working system with a stepper motor and demonstrate the importance of such an algorithm in elastic structure robot control.

robĂłtica 118, 1.o Trimestre de 2020

THEORY Scalar velocity, acceleration and jerk management Knowing that jerk is the derivative of acceleration, acceleration the derivative of velocity and velocity the derivative of position, we end up with a cubic position expression for the stages where j is not 0, a quadratic expression where a is constant and a linear expression in the stages where a is 0: The following graphs represent the evolution of a scalar position (x) from an origin if we setup a movement of a speciďŹ c distance with a motion rule that has a speciďŹ ed jerk (j), a max acceleration (amax) and a max velocity (vmax):

For the constant velocity stage:


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