Hybrid control for navigation of shape-accelerated underactuated balancing systems

Abstract

Abstract-This paper presents a hybrid control strategy for navigation of shape-accelerated underactuated balancing systems with dynamic constraints. It extends the concept of sequential composition to perform discrete state-based switching between asymptotically convergent control policies to produce a globally asymptotically convergent feedback policy. The individual control policies consists of an external trajectory planner, a shape trajectory planner, an external trajectory tracking controller and a balancing controller. The paper also presents an integrated planning and control procedure, wherein standard graph-search algorithms are used to plan for the sequence of control policies that will help the system achieve a navigation goal. Simulation results of the 3D ballbot system navigating an environment with static obstacles to reach the goal position are also presented.

Integrated planning and control for graceful navigation of shape-accelerated underactuated balancing mobile robots

“…2. Each motion policy consists of a reference state trajectory called a motion primitive, a time-varying feedback trajectory tracking controller and a time-varying domain that is verified to be asymptotically convergent [10]. …”

“…The motion policy domains D(t) are defined as geometric domains in 4D position state space, i.e., (x, y,ẋ,ẏ), similar to the ones in [10]. The motion policies use the control architecture in Fig.…”

“…Though the procedure presented in [10] was capable of navigating an environment with obstacles, the resulting robot motion was not graceful. This is primarily due to the discrete switching between the control policies.…”

“…Graph search algorithms were used to find a sequence of control policies to achieve the navigation task. In our previous work [10], we extended this procedure to balancing mobile robots like the ballbot.…”

Learning Sequential Composition Control

“…Applications of sequential composition include, for instance, balancing of an underactuated system [2], navigation of an autonomous mobile robot [3], [4], navigation of fully actuated dynamical systems through cluttered environments [5], control of cooperative systems [6], etc. The standard sequential composition framework has been extended in several ways.…”