Compliant control of Uni/ Multi- robotic arms with dynamical systems

Accomplishment of many interactive tasks hinges on the compliance of humans. Humans demonstrate an impressive capability of complying their behavior and more particularly their motions with the environment in everyday life. In humans, compliance emerges from different facets. For example, many daily activities involve reaching for grabbing tasks, where compliance appears in a form of coordination. Humans comply their hands’ motions with each other and with that of the object not only to establish a stable contact and to control the impact force but also to overcome sensorimotor imprecisions. Even though compliance has been studied from different aspects in humans, it is primarily related to impedance control in robotics. In this thesis, we leverage the properties of autonomous dynamical systems (DS) for immediate re-planning and introduce active complaint motion generators for controlling robots in three different scenarios, where compliance does not necessarily mean impedance and hence it is not directly related to control in the force/velocity domain. In the first part of the thesis, we propose an active compliant strategy for catching objects in flight, which is less sensitive to the timely control of the interception. The soft catching strategy consists in having the robot following the object for a short period of time. This leaves more time for the fingers to close on the object at the interception and offers more robustness than a “hard” catching method in which the hand waits for the object at the chosen interception point. We show theoretically that the resulting DS will intercept the object at the intercept point, at the right time with the desired velocity direction. Stability and convergence of the approach are assessed through Lyapunov stability theory. In the second part, we propose a unified compliant control architecture for coordinately reaching for grabbing a moving object by a multi-arm robotic system. Due to the complexity of the task and of the system, each arm complies not only with the object’s motion but also with the motion of other arms, in both task and joint spaces. At the task-space level, we propose a unified dynamical system that endows the multi-arm system with both synchronous and asynchronous behaviors and with the capability of smoothly transitioning between the two modes. At the joint space level, the compliance between the arms is achieved by introducing a centralized inverse kinematics (IK) solver under self-collision avoidance constraints; formulated as a quadratic programming problem (QP) and solved in real-time. In the last part, we propose a compliant dynamical system for stably transitioning from free motions to contacts. In this part, by modulating the robot's velocity in three regions, we show theoretically and empirically that the robot can (I) stably touch the contact surface (II) at a desired location, and (III) leave the surface or stop on the surface at a desired point.