Abstract
Variable-stiffness actuation exhibits promising features for obtaining human-like behavior and safer human robot physical interaction. Task planning and closed-loop control of these systems pose many challenges due to their complicated structure and the need of satisfying many constraints during task execution. This paper introduces a framework for the design and numerical solution of time-optimal control problems for variable-stiffness-actuated (VSA) systems. Two different time-optimal control problems, namely, minimum time for target performance and minimum time for maximum performance, are formally defined, and methods for solving them are presented based on existing numerical software tools for nonlinear optimization. Two experimental case studies, focusing on ball-throwing tasks with antagonistically actuated VSA systems, are used to test the presented methods and show their validity.
Highlights
In the structured environment of factories, robots outperform human workers in tasks requiring fast, repetitive and precise manipulation
The nonlinear model predictive control (NMPC) controller acted with a sampling interval Ts = 20 ms, reading motor and link positions from highresolution capacitive incremental encoders, and generated the motor reference positions θd in real time, in order to track the robot motion planned by the optimal control problem (OCP)
1) Experimental setup: We employed another experimental setup for solving the minimum time for maximum performance problem, in order to demonstrate the applicability of our methodologies for different types of variable stiffness actuated (VSA) robots
Summary
In the structured environment of factories, robots outperform human workers in tasks requiring fast, repetitive and precise manipulation. Braun et al [9] formulated motor trajectory generation of variable stiffness actuated (VSA) robots as an optimal control problem (OCP). We present a general framework for the timeoptimal motion planning of VSA robots with any kind of topology, subject to any type of set-membership constraints on inputs and states (e.g., limits on actuator torques and velocities, maximum extension or compression of the elastic elements, maximum link speeds, etc.). The second, “minimum time for maximum performance” (Section IV), has the objective of minimizing the time in which the robot motion happens, at the same time maximizing the obtainable performance (e.g., minimize the time for the throwing motion, while throwing the object at the maximum achievable distance for the given robot configuration and constraints) For both kinds of problems, which in general can be formulated as nonlinear programs, the solution is determined numerically, by using the ACADO Toolkit [26]. In order to find them, a numerical solution of the OCP (6) is obtained (for the shown experimental results, using the ACADO Toolkit), as described in the following subsection
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