Dynamic movement primitives (DMPs) were proposed as an efficient way for learning and control of complex robot behaviors. They can be used to represent point-to-point and periodic movements and can be applied in Cartesian or in joint space. One problem that arises when DMPs are used to define control policies in Cartesian space is that there exists no minimal, singularity-free representation of orientation. In this paper we show how dynamic movement primitives can be defined for non minimal, singularity free representations of orientation, such as rotation matrices and quaternions. All of the advantages of DMPs, including ease of learning, the ability to include coupling terms, and scale and temporal invariance, can be adopted in our formulation. We have also proposed a new phase stopping mechanism to ensure full movement reproduction in case of perturbations.
Abstract-The framework of dynamic movement primitives contains many favorable properties for the execution of robotic trajectories, such as indirect dependency on time, response to perturbations, and the ability to easily modulate the given trajectories, but the framework in its original form remains constrained to the kinematic aspect of the movement. In this paper we bridge the gap to dynamic behavior by extending the framework with force/torque feedback. We propose and evaluate a modulation approach that allows interaction with objects and the environment. Through the proposed coupling of originally independent robotic trajectories, the approach also enables the execution of bimanual and tightly coupled cooperative tasks. We apply an iterative learning control algorithm to learn a coupling term, which is applied to the original trajectory in a feedforward fashion and thus modifies the trajectory in accordance to the desired positions or external forces. A stability analysis and results of simulated and real-world experiments using two KUKA LWR arms for bimanual tasks and interaction with the environment are presented. By expanding on the framework of dynamic movement primitives, we keep all the favorable properties, which is demonstrated with temporal modulation and in a two-agent obstacle avoidance task.
This investigation was designed to (a) develop an individualized mechanical model for measuring aerodynamic drag (F(d) ) while ski racing through multiple gates, (b) estimate energy dissipation (E(d) ) caused by F(d) and compare this to the total energy loss (E(t) ), and (c) investigate the relative contribution of E(d) /E(t) to performance during giant slalom skiing (GS). Nine elite skiers were monitored in different positions and with different wind velocities in a wind tunnel, as well as during GS and straight downhill skiing employing a Global Navigation Satellite System. On the basis of the wind tunnel measurements, a linear regression model of drag coefficient multiplied by cross-sectional area as a function of shoulder height was established for each skier (r > 0.94, all P < 0.001). Skiing velocity, F(d) , E(t) , and E(d) per GS turn were 15-21 m/s, 20-60 N, -11 to -5 kJ, and -2.3 to -0.5 kJ, respectively. E(d) /E(t) ranged from ∼5% to 28% and the relationship between E(t) /v(in) and E(d) was r = -0.12 (all NS). In conclusion, (a) F(d) during alpine skiing was calculated by mechanical modeling, (b) E(d) made a relatively small contribution to E(t) , and (c) higher relative E(d) was correlated to better performance in elite GS skiers, suggesting that reducing ski-snow friction can improve this performance.
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