A clear trend in robotics today is the emerged use of collaborative robots which have evolved as one of the key drivers in Industry 4.0. A crucial factor to address as the robots are operating in human environments is the safety aspect. Often, safety conditions can be encoded as limits on velocities or accelerations and to handle these in the motion control is of significant importance.
The use of stable dynamical systems as models has become a popular paradigm for motion planning in robotics and a widely spread formulation is Dynamical Movement Primitives (DMPs). DMPs have a compact and elegant formulation, are sufficiently flexible to create complex behaviors and can be learned from data. Moreover, they allow for reactive planning by introduction of sensory feedback in the planning process. In this way, the trajectory can, for instance, adjust to unpredictable events and obstacles in the environment or be modified online to improve the task performance according to a given metric.
Allowing online modifications of the trajectory, and thereby making it less predictable, can however raise problems when constraints on velocity and acceleration need to be accommodated in the motion planning. Direct saturation in the controller leads to divergence of the system trajectory from the target trajectory generated by the dynamical system and a better approach would be to instead take the constraints into account already in the motion planning stage.
In this seminar, the problem of online adapting a nominal trajectory of a DMP to respect velocity and acceleration constraints while preserving the original trajectory path is considered. A novel filter based on a potential function is presented which guarantees the trajectory to stay within prescribed velocity bounds while preserving the path. Furthermore, an extension of the filter is given which enables imposing both velocity and acceleration constraints, based on transforming the constraints into one-dimensional path traversal constraints. The effectiveness of the approach will be demonstrated through simulation and experimental results.