Abstractions and Algorithms for Cooperative Multiple Robot Planar Manipulation

Abstract

Abstract-In this paper, we will study abstractions and algorithms for planar manipulation systems using two cooperating robots under uncertainties. We propose a formal framework for developing abstractions, which are simpler models of the original systems that preserve properties of interest to facilitate the development of planning and control algorithms. Our abstractions are derived from robust motion primitives that correspond to control inputs leading to system trajectories which preserve the properties of interest under uncertainties. We then use the proposed framework to construct an abstraction and design planning and control algorithms for a multiple robot cooperative manipulation system. Finally, we present experimental results to validate our approach. I. INTRODUCTIONIt is well known that conventional approaches to robotic manipulation, where deliberative planning is augmented by feedback controllers, are difficult to implement except in the simplest of cases. This is primarily because of non smooth dynamics engendered by frictional contacts and uncertainties in the parameters governing the contact dynamics. Experiments in robotic juggling [8], locomotion [11,25], non prehensile manipulation [35], manipulation via caging (Fig. 2) [13], and part-feeding [29] have shown that feedback controllers, behaviors or designs, which are specially designed to preserve a specific set of properties (e.g., convergence to sub manifolds or limit sets), are more robust to uncertainties than those that follow optimally-planned trajectories in the full state space. Indeed, this philosophy of designing components that each drive the system to a state that satisfies a specific property is used extensively in manufacturing operations, where designers carefully structure the environment to ensure that devices like bowl-feeders [14], conveyors [1], traps [5], and pick-andplace arms work in concert to accomplish the given task. Many paradigms in robotics such as caging [7], the onejoint-over-conveyor part positioning [1], and remote-centerof-compliance assembly [12] are also illustrative of this philosophy. While these examples are arguably special-purpose solutions, they illustrate a very important point. By designing planners/controllers that drive the system to submanifolds in the state space, one can derive abstractions of complex processes, i.e., conceptual models that are much simpler than the complex real-world system, that lend themselves to the design of algorithms that can reason about these abstractions and the composition of these complex processes.We use the simple example of multi-fingered or multirobot manipulation in the plane via caging to illustrate the role of abstractions and algorithms (Fig. 2). The modeling

Timed abstractions for distributed cooperative manipulation

“…Regarding robotic manipulation, high level planning techniques have been proposed in Yamashita et al (2003), Cheng et al (2009), Lionis and Kyriakopoulos (2005) using common planning methods like potential fields in the configuration space and A * algorithms. In Lionis and Kyriakopoulos (2005) the motion planning problem for a group of unicycles manipulating a rigid body is addressed and in Cheng et al (2009) an abstraction methodology is introduced; LTL specifications are employed in Tsiamis et al (2015a), where two mobile robots transport an object in a leader-follower scheme. Additionally, temporal logic formulas are utilized in Muthusamy and Kyrki (2014) for dexterous manipulation through robotic fingers and in He et al (2015) for single manipulation tasks, without, however, incorporating the dynamics of the robotic arm in the abstracted model.…”

Combining motion planning and optimization for flexible robot manipulation

“…However, the basic challenge with these approaches is that optimality is fundamentally harder to achieve than feasibility when computing a plan. In contrast, model-based planners learn and use dynamic models to identify collision-free paths between start and goal states [4], [5], [19]. The drawback to these methods is that in giving up the pursuit of an optimal plan they also remove the ability to easily specify abstract goals.…”

Distributed cooperative manipulation under timed temporal specifications

“…Regarding robotic manipulation, high level planning techniques have been proposed in [23]- [25] using common planning methods like configuration space potential fields and A * algorithms. In [25] the motion planning problem for a group of unicycles manipulating a rigid body is addressed and in [24] an abstraction methodology is introduced; LTL specifications are employed in [26], where two mobile robots transport an object in a leader-follower scheme. Additionally, temporal logic formulas are utilized in [27] for dexterous manipulation through robotic fingers and in [28] for single manipulation tasks, without, however, incorporating the dynamics of the robotic arm in the abstracted model.…”