Simultaneous Stiffness and Trajectory Optimization for Energy Minimization of Pick-and-Place Tasks Of SEA-Actuated Parallel Kinematic Manipulators

Thomas Kordik, Hubert Gattringer, and Andreas Müller
J. Comput. Nonlinear Dynam. Aug 2025, 20(8): 081008
​https://doi.org/10.1115/1.4068321

A major field of industrial robot applications deals with repetitive tasks that alternate between operating points. For these so-called pick-and-place operations, parallel kinematic manipulators (PKM) are frequently employed. These tasks tend to automatically run for a long period of time and therefore minimizing energy consumption is always of interest. As recent research addresses the use of elastic elements, this paper explores the possibilities of minimizing energy consumption of pick-and-place task performing PKM that are driven by series elastic actuators (SEA). The basic idea is to excite eigenmotions that result from the actuator springs and exploit their oscillating characteristics. To this end, a prescribed cyclic pick-and-place operation is analyzed and a dynamic model of SEA driven PKM is derived. Subsequently, an energy minimizing optimal control problem is formulated where operating trajectories as well as SEA stiffnesses are optimized simultaneously. Here, optimizing the actuator stiffness does not account for variable stiffness actuators. It serves as a tool for the design and dimensioning process. The hypothesis on energy reduction is tested on two (parallel) robot applications where redundant actuation is also addressed. The results confirm the validity of this approach.