Fig 6 - uploaded by Shervin Ghasemlou
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An alternative, more direct plan that solves the problem of navigating Figure 4's robot to its charger. This plan is an homomorphic solution.
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We address problems underlying the algorithmic question of automating the co-design of robot hardware in tandem with its appo-site software. Specifically, we consider the impact that degradations of a robot's sensor and actuation suites may have on the ability of that robot to complete its tasks. Expanding upon prior work that addresses similar que...
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We address problems underlying the algorithmic question of automating the co-design of robot hardware in tandem with its apposite software. Specifically, we consider the impact that degradations of a robot's sensor and actuation suites may have on the ability of that robot to complete its tasks. We introduce a new formal structure that generalizes...
Citations
... For the former, we must be able to verify that a given instance of DECDM is a YES instance efficiently. For any positive instance, there is a solution no larger than W via Theorem 27 of [10], the argument therein carrying over when considering plans subject to some design cost c(P ) ≤ k. Such a plan, which is itself state-determined, can be used as a certificate. ...
... Then the design-time sensor choice becomes a question of committing to a particular transformation. Previously in [10], we formalized the idea of these kinds of transformations that operate on the sets of labels borne by observation edges by introducing the notion of observation maps: ...
... State determined forms: The idea of a state-determined form was developed in [28] and [10]. Its importance, prior to the present paper, had been mainly abstract and conceptual. ...
Assuming one wants to design the most cost-effective robot for some task, how difficult is it to choose the robot’s actuators? This paper addresses that question in algorithmic terms, considering the problem of identifying optimal sets of actuation capabilities to allow a robot to complete a given task. We consider various cost functions which model the cost needed to equip a robot with some capabilities, and show that the general form of this problem is NP-hard, confirming what many perhaps have suspected about this sort of design-time optimization. As a result, several questions of interest having both optimality and efficiency of solution is unlikely. However, we also show that, for some specific types of cost functions, the problem is either polynomial time solvable or fixed-parameter tractable.
... In the current work, we use procrustean graphs [10], [17] to encode planning problems and plans that solve them. The notion of plan here refers to a p-graph that guides the robot within the planning problem to achieve its goal. ...
... We also present the concepts of label maps that we use to model alterations to a procrustean graph, and a refinement relation that we use to navigate between different designs. These are condensed versions of detailed definitions that appear in our prior studies [10], [17]. ...
... To decide if there exists a solution for a planning problem (G,V goal ), one can first convert the p-graph to its equivalent state determined expansion [10], and then run a backchaining algorithm on G. The algorithm establishes a solution incrementally by identifying the states in the planning problem from which we can guarantee to reach the goal, starting from V goal . ...
This paper aims to improve the practical scala-bility of automated tools to assist in designing robots. Such problems rapidly become intractable because the underlying design space is immense. We consider a specific type of design tool addressed in prior work, which constructs a representation of the destructiveness boundary in the space of robot designs. This prior work showed that a legible representation, specifically a decision tree, of this boundary can illuminate which elements of a sensing or actuation system are most important for enabling the robot to complete its task. In that context, the robot's interaction with the world is represented as procrustean graph, and the space of robot designs is represented by the space of label maps that rewrite the labels on that graph. In this paper, we expand upon those results by showing how domain knowledge can enable such tools to find solutions to more complex problems within a reasonable time frame. Specifically, we propose three different scenarios, expressed as constraints on the p-graph and on the label maps, under which the learning algorithm to identify the destructiveness boundary can converge quickly to high accuracy results for problems at larger scales than the prior, general-purpose algorithm. The conditions for each of these scenarios are easily verifiable and the set of problems that fall under each is rich enough to encompass several interesting problems. Experimental results demonstrate the effectiveness of the proposed methods.
... Preliminary versions of this work appeared in 2016 at RSS ( Saberifar et al., 2016) and WAFR ( Ghasemlou et al., 2016). ...
We address problems underlying the algorithmic question of automating the co-design of robot hardware in tandem with its apposite software. Specifically, we consider the impact that degradations of a robot’s sensor and actuation suites may have on the ability of that robot to complete its tasks. We introduce a new formal structure that generalizes and consolidates a variety of well-known structures including many forms of plans, planning problems, and filters, into a single data structure called a procrustean graph, and give these graph structures semantics in terms of ideas based in formal language theory. We describe a collection of operations on procrustean graphs (both semantics-preserving and semantics-mutating), and show how a family of questions about the destructiveness of a change to the robot hardware can be answered by applying these operations. We also highlight the connections between this new approach and existing threads of research, including combinatorial filtering, Erdmann’s strategy complexes, and hybrid automata.
... Preliminary versions of this work appeared in 2016 at RSS ( Saberifar et al., 2016) and WAFR ( Ghasemlou et al., 2016). ...
We address problems underlying the algorithmic question of automating the co-design of robot hardware in tandem with its apposite software. Specifically, we consider the impact that degradations of a robot's sensor and actuation suites may have on the ability of that robot to complete its tasks. We introduce a new formal structure that generalizes and consolidates a variety of well-known structures including many forms of plans, planning problems, and filters, into a single data structure called a procrustean graph, and give these graph structures semantics in terms of ideas based in formal language theory. We describe a collection of operations on procrustean graphs (both semantics-preserving and semantics-mutating), and show how a family of questions about the destructiveness of a change to the robot hardware can be answered by applying these operations. We also highlight the connections between this new approach and existing threads of research, including combinatorial filtering, Erdmann's strategy complexes, and hybrid automata.
This article examines the selection of a robot’s actuation and sensing hardware to minimize the cost of that design while ensuring that the robot is capable of carrying out a plan to complete a task. Its primary contribution is in the study of the hardness of reasonable formal models for that minimization problem. Specifically, for the case in which sensing hardware is held fixed, we show that this algorithmic design problem is NP-hard even for particularly simple classes of cost functions, confirming what many perhaps have suspected about this sort of design-time optimization. We also introduce a formalism, based on the notion of label maps, for the broader problem in which the design space encompasses choices for both actuation and sensing components. As a result, for several questions of interest, having both optimality and efficiency of solution is unlikely. However, we also show that, for some specific types of cost functions, the problem is either polynomial-time solvable or fixed-parameter tractable.
Note to Practitioners
—Despite the primary results being theoretical and, further, taking the form of bad news, this article still has considerable value to practitioners. Specifically, assuming that one has been employing heuristic or approximate solutions to robot design problems, this article serves as a justification for doing so. Moreover, it delineates some circumstances in which one can, in a sense, do better and achieve genuine optima with practical algorithms.
