Composing motion primitives under disturbances: a switched systems approach

Date
2018
Journal Title
Journal ISSN
Volume Title
Publisher
University of Delaware
Abstract
Robots operating in the real world are expected to encounter a wide range of exogenous input signals due to contact or other types of interaction with a possibly time-varying, stochastic environment. Depending on the task, external signals may represent commands that need to be followed or disturbances that must be attenuated. A diverse collection of suitable primitive motions, and the capability to switch among them, can provide a sufficiently rich repertoire of behaviors for adapting to or compensating for such signals. This dissertation provides a method to generate complex goal-oriented robot motions that are robust to disturbances and capable of adapting to exogenous signals by coordinated switching among a collection of dynamical motion primitives (DMPs)---characterized by dynamical systems with equilibria. ☐ The planning-control architecture used in this dissertation---which is also fairly pervasive in robotics---consists of a high-level planner and a low-level controller. The high-level planner is equipped with a discrete set of motion primitives and it makes logic-based decisions to generate a motion plan. The low-level controller receives this motion plan and executes it on the robot. Constraints arising from the dynamics may inhibit the robot from executing arbitrary motion plans, thereby making it necessary to equip the high-level planner with the capability to reason about these dynamic limitations. This dissertation exploits and expands on existing switched system's literature to encode these dynamic limitations as an upper bound on the frequency of switching among the motion primitives. These easy to implement constraints on the switching frequency, when respected by the high-level planner, result in motion plans compatible with the low-level dynamics of the robot, even in the presence of disturbances. ☐ In this dissertation, the above framework is particularized to dynamically-stable bipedal robots that ambulate through periodic interactions with their environment. The biped is modeled as a system with impulsive effects (SIE), a sub-class of hybrid systems, and the gait is modeled as an exponentially stable periodic limit cycle in the state space of the SIE. Implementing the above framework for motion planning of a biped entails switching among multiple such limit-cycle gaits---a very challenging problem accounting for the high-dimensional, nonlinear, and hybrid dynamics that the biped possesses. This task can be facilitated by switching among the Poincar\'e map of each limit cycle, giving rise to a discrete switched system with multiple equilibria. Exploiting the switched systems framework discussed above, bounds for switching frequency are obtained to generate safely executable motion plans for navigation of a 3D biped across an environment cluttered by obstacles, and gait adaptation of a 3D biped in human-robot cooperative teams. ☐ In summary, the main contributions of this dissertation are: (1) a general framework which provides guarantees for well-behaved switching among DMPs despite the presence of persistent disturbances; and (2) the application of this framework to perform gait adaptation in response to high-level objectives, for a high-dimensional bipedal robot model with limit-cycle gait primitives. It is worth noting, that even though the switching framework is particularized to bipedal robots in this dissertation, it can be used for any robot with asymptotically stable DMPs.
Description
Keywords
Citation