On Trajectory Generation for Robots

Sammanfattning: A fundamental problem in robotics is the generation of motion for a task. How to translate a task to a set of movements is a non-trivial problem. The complexity of the task, the capabilities of the robot, and the desired performance, affect all aspects of the trajectory; the sequence of movements, the path, and the course of motion as a function of time.This thesis is about trajectory generation and advances the state of the art in several directions. Special attention to trajectories in constrained situations when interaction forces are involved is paid. We bring a control perspective to trajectory generation and propose novel solutions for online trajectory generation with a rapid response to sensor inputs. We formulate and find optimal trajectories for various problems, closing the gap between path planning and trajectory generation. The inverse problem of finding the control signal corresponding to a desired trajectory is investigated and we extend the applicability of an existing algorithm to a broader class of problems.To collect human-generated trajectories involving force interactions, we propose a method to join two robotic manipulators to form a haptic interface for task demonstration. Furthermore, fast algorithms for fixed-time point-to-point trajectory generation are investigated. More importantly, two optimal closed-loop trajectory generation methods are proposed. We derive an optimal controller for the fixed-time trajectory-generation problem with a minimum-jerk cost functional. The other method is based on Model Predictive Control, which allows a more generic form of system dynamics and constraints. In addition, a ball-and-finger system is modeled for studying trajectory generation where interaction plays an important role. Efficient movements for rotating the ball are numerically computed and simulated.Iterative Learning Control (ILC) finds a proper control signal for obtaining a desired trajectory. We derive frequency-domain criteria for the convergence of linear ILC on finite-time intervals that are less restrictive than existing ones in the literature.