Online Trajectory Generation

Generating robot motion trajectories online and instantaneously is one of the important features of robot motion control systems to let robots safely act in human environments. Recently, a framework of online trajectory generation algorithms was developed that allows generating trajectories from arbitrary states of motion within less than one millisecond while taking into account dynamic constraints. Using this framework, robots become able to react instantaneously and deterministically to unforeseen sensor signals and events. Moreover, new features such as instantaneous reference frame changes and switching from sensor-guided motion control to trajectory-following motion control on-the-fly without exciting vibrations become possible. These trajectory generation algorithms have been freely released as part of the Reflexxes Motion Libraries and are freely available to research and education institutions. Type II is released under the GNU Lesser General Public License (LGPL V3.0). Besides introducing the basics of this new technology, this half-day hands-on tutorial intends to show how these new features are used in real robotic systems. The audience will program own applications in virtual environments, which include scenarios of visual-servo control, switched-system control, high-level online task planning, and human-robot collision avoidance.

New Robot Motion Control Functions

The Reflexxes Motion Libraries enable new opportunities in sensor-based motion control. Robots and servo drive control systems can instantaneously react to unforeseen sensor events:


Online motion planning has drawn increasing interest, as robots have started to gain the sensorial and actuation capabilities to effectively perceive their environment. Numerous interaction control and motion schemes have been developed based on Reflexxes software, and some have already reached the industrial sector.

Contents and Objectives

This hands-on tutorial will

  1. introduce the mathematical foundations of the used algorithmic concepts
  2. discuss use-cases and applications, and
  3. allow and support hands-on programming of own applications in a virtual environment.

Special attention will be given to implementations of new robot motion control features:

  • Deterministic, instantaneous reaction motions to sensor signals taking into account current dynamic capabilities
  • Simple and robust visual servo control allowing deterministic reactions to unsteady signals or even failures of the vision system
  • Unforeseen, instantaneous switchings of reference frames and control state spaces
  • Deterministic and stable reaction motions to sensor failures
  • Primitive-based programming with continuous motions during discrete transitions between primitives
  • Stable hybrid switched-system control

The online trajectory generation algorithms of the Reflexxes Motion Libraries are the first ones that allow computing jerk-limited robot motions from arbitrary initial states of motion while considering the current dynamic capabilities of robots. This is an important feature for classic industrial robot control architectures, servo drive control units, as well as for cutting edge robots with variable-stiffness or serial-elastic actuators in order to achieve deterministic reaction behaviors to sensor signals and events.