Timed trajectory generation using dynamical systems: Application to a Puma arm

We present an attractor based dynamics that autonomously generates trajectories with stable timing (limit cycle solutions), stably adapted to changing online sensory information. Autonomous differential equations are used to formulate a dynamical layer with either stable fixed points or a stable limit cycle. A neural competitive dynamics switches between these two regimes according to sensorial context and logical conditions. The corresponding movement states are then converted by simple coordinate transformations and an inverse kinematics controller into spatial positions of a robot arm. Movement initiation and termination is entirely sensor driven. In this article, the dynamic architecture was changed in order to cope with unreliable sensor information by including this information in the vector field. We apply this architecture to generate timed trajectories for a Puma arm which must catch a moving ball before it falls over a table, and return to a reference position thereafter. Sensory information is provided by a camera mounted on the ceiling over the robot. A flexible behavior is achieved. Flexibility means that if the sensorial context changes such that the previously generated sequence is no longer adequate, a new sequence of behaviors, depending on the point at which the changed occurred and adequate to the current situation emerges. The evaluation results illustrate the stability and flexibility properties of the dynamical architecture as well as the robustness of the decision-making mechanism implemented. © 2008 Elsevier B.V. All rights reserved.