A Time Optimal Trajectory Generation Method for a Flatness Based Controlled Flexible Link Robot
Sprache des Vortragstitels:
EACS 2012, 5th European Conference on Structural Control.
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This paper presents a highly efficient method for time optimal control of an articulated robot with two flexible links and three joints. The main focus of this contribution is laid on the trajectory planning for very fast movements of the lightweight and flexible manipulator. A basic feature of the presented realtime algorithm is that a complete dynamic model, including elasticity and friction, is considered such that limits on actuator torques and joint velocities are not exceeded and vibrations are suppressed.
Therefore, a so called lumped element model is used which is shown to be a sufficiently accurate representation of the system. It is assumed that the elastic deformations of the beams can be approximated by linear springs and dampers resulting in a flat system with the joint angles as flat output.
In order to generate time optimal trajectories for this flat output, an open loop optimal control problem is formulated by projecting the system dynamics on a predefined geometric path. Additionally, the property that all system states and inputs can be expressed as functions of the flat output and its derivatives is used to define path constraints for motor torques, motor velocities, arm torques and the change rate of arm torques. Techniques known from nonlinear model predictive control (NMPC) together with a fourth order B-Spline parameterization are utilized to subdivide the original optimal control problem to be able to compute trajectories in realtime. Additionally, sequential quadratic programming (SQP) is applied to solve the resulting nonlinear optimization problem (NLP) cyclically.
Finally, a common flatness based feedback control is applied to track the generated reference trajectories. Experimental results for a time optimal movement along a straight line in Cartesian space confirm that the resulting trajectories are not violating any path constraints.