{"id":625,"date":"2021-06-18T02:55:32","date_gmt":"2021-06-18T06:55:32","guid":{"rendered":"https:\/\/blogs.sw.siemens.com\/plm-components\/?p=625"},"modified":"2026-03-26T08:03:47","modified_gmt":"2026-03-26T12:03:47","slug":"kineoworks-step-by-step-working-with-trajectories","status":"publish","type":"post","link":"https:\/\/blogs.sw.siemens.com\/plm-components\/kineoworks-step-by-step-working-with-trajectories\/","title":{"rendered":"KineoWorks step-by-step #3: working with trajectories"},"content":{"rendered":"\n

KineoWorks<\/a>TM<\/sup> is a software component that automatically computes collision-free motion, solving complex path-planning problems in applications such as robotic collision-free trajectory optimization. In this series of articles, Etienne Ferr\u00e9, Development Director of Kineo components, describes some of the key steps that you can easily implement to develop a sophisticated robotics simulation.<\/p>\n\n\n\n

Part 3: Working with Trajectories<\/h2>\n\n\n\n

So far in this series, we have described processes for path planning<\/a> and building a robot<\/a>. This article takes a closer look at trajectories<\/em> that describe the movement of a kinematic system over time. But first, a quick reminder about paths\u2026<\/p>\n\n\n\n

In KineoWorks, a path is described by a sequence of configurations. Elementary paths made of pairs of configurations are called direct paths.<\/p>\n\n\n

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\"A<\/figure><\/div>\n\n\n

The purpose of a path is to connect a start configuration to a goal configuration in a configuration space. You can associate a configuration with any 1-dimensional position between 0.0 and the path length.<\/p>\n\n\n\n

Path length meaning<\/h3>\n\n\n\n

Path length is usually the total distance along the path in a configuration space, but not always<\/em>: it mainly depends on the path steering method. Most of the time, it is safe to assume that the lower the length is, the shorter the path is. This allows you to optimize paths, for instance, using length as a criterion. But length is not suitable for representing durations as it doesn\u2019t describe where the system is at a given time<\/em>. This is one limitation of using paths.<\/p>\n\n\n\n

Path guarantee on continuity<\/h3>\n\n\n\n

A path is guaranteed to be continuous in position because losing position continuity would break the connection between the start and the goal configurations. However, there is no such guarantee of continuity of the derivative.<\/p>\n\n\n\n

If you interpret the derivative of a path as velocity, you are not guaranteed continuous velocity. Typically, a sequence of direct paths, with a linear steering method, going in different directions will jump from a constant velocity in one direction to a constant velocity in another direction. You would not be able to run such a path on a real system which requires at least a continuous velocity. This is a second limitation of using paths.<\/p>\n\n\n

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An example of a path with two direct paths.
With a linear steering method, the velocity on the y axis jumps from a positive value to a negative value<\/figcaption><\/figure><\/div>\n\n\n

Executing a path on a real system<\/h3>\n\n\n\n

Despite these limitations, as a solution to a path planning problem, a path does the job: it connects start and goal configurations. A path is all we need to make this connection in the valid configuration space. However, as seen above, a path in general does not describe how the system should move over time, because it does not take into account maximum velocity, maximum acceleration, continuity constraints and other parameters of the real system.<\/p>\n\n\n\n

A solution to this problem is to use specific velocity profiles such as the trapezoidal velocity profile. Such profiles allow a path to be followed exactly while guaranteeing a continuous velocity at one cost: the velocity must be null at waypoints when the direction changes. Such profiles can be managed by a 3rd party robot controller (requiring only path configurations as input) or they can be simulated with the corresponding steering method. The trapezoidal steering method is an example where the length of a path is no longer a distance because it simulates motion over time.<\/p>\n\n\n

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With a trapezoidal steering method, the velocity becomes continuous<\/figcaption><\/figure><\/div>\n\n\n

The solution above is not always satisfactory because:<\/p>\n\n\n\n