# A Dynamic Programming Approach for Time‐Optimal Path Following of Robots Considering Speed Dependent Torque Constraints

A Dynamic Programming Approach for Time‐Optimal Path Following of Robots Considering Speed... Time‐optimal path following, i.e. moving a robot's end‐effector optimally along a specified geometric path, is a very important and well discussed problem in robotics. Nevertheless, most of the existing approaches concerning this topic neglect the speed dependency of torque constraints. The present paper presents a method for taking such constraints into account within a dynamic programming approach. To this end, the problem is treated in parameter space. This allows for an optimal use of existing resources. Due to the demanding constraints, precise mathematical models of the robots are indispensable. A satisfying match between model and real system can usually be achieved by parameter identification. For this purpose, it is a common way to derive the equations of motion using nominal parameters (masses, position of center of gravity, inertia and friction parameters), rewrite the equations in terms of linearly independent base parameters, and determine them with the help of measurements. Nevertheless, a parametrization of the motor torques has to be introduced in order to be able to consider their constraints within the optimization. In contrast to this, we present a general toolchain, based on the Projection Equation that directly derives the base parameter representation and furthermore the coefficients of the parametrized equations of motion. A verification in terms of a numerical example for a six‐axis industrial robot demonstrate why speed dependent torque constraints are preferable over constant torque constraints for time‐optimal robot trajectories. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

# A Dynamic Programming Approach for Time‐Optimal Path Following of Robots Considering Speed Dependent Torque Constraints

, Volume 17 (1) – Jan 1, 2017
2 pages

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Publisher
Wiley
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710048
Publisher site
See Article on Publisher Site

### Abstract

Time‐optimal path following, i.e. moving a robot's end‐effector optimally along a specified geometric path, is a very important and well discussed problem in robotics. Nevertheless, most of the existing approaches concerning this topic neglect the speed dependency of torque constraints. The present paper presents a method for taking such constraints into account within a dynamic programming approach. To this end, the problem is treated in parameter space. This allows for an optimal use of existing resources. Due to the demanding constraints, precise mathematical models of the robots are indispensable. A satisfying match between model and real system can usually be achieved by parameter identification. For this purpose, it is a common way to derive the equations of motion using nominal parameters (masses, position of center of gravity, inertia and friction parameters), rewrite the equations in terms of linearly independent base parameters, and determine them with the help of measurements. Nevertheless, a parametrization of the motor torques has to be introduced in order to be able to consider their constraints within the optimization. In contrast to this, we present a general toolchain, based on the Projection Equation that directly derives the base parameter representation and furthermore the coefficients of the parametrized equations of motion. A verification in terms of a numerical example for a six‐axis industrial robot demonstrate why speed dependent torque constraints are preferable over constant torque constraints for time‐optimal robot trajectories. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

### Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

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