Chapman’s paper, “Planning for Conjunctive Goals,” has been widely acknowledged as a major step towards understanding the nature of nonlinear planning, and it has been one of the bases of later work by others—but it is not free of problems. This paper discusses the following problems with modal truth and the modal truth criterion. 1. It is NP-hard to tell, given a plan P and a ground atom p, wh...

In this paper, we examine how the complexity of domain-independent planning with STRIPS-style operators depends on the nature of the planning operators. We show conditions under which planning is decidable and undecidable. Our results on this topic solve an open problem posed by Chapman [5], and clear up some difficulties with his undecidability theorems. For those cases where planning is decid...

In this paper we address the constructive controllability problem for drift-free, leftinvariant systems on nite-dimensional Lie groups with fewer controls than state dimension. We consider small ( ) amplitude, low-frequency, periodically time-varying controls and derive average solutions for system behavior. We show how the pth-order average formula can be used to construct open-loop controls f...

In this paper, we show that in the best-known version of the blocks world (and several related versions), planning is difficult, in the sense that finding an optimal plan is NP-hard. However, the NP-hardness is not due to deleted-condition interactions, but instead due to a situation which we call a deadlock. For problems that do not contain deadlocks, there is a simple hill-climbing strategy t...

This paper studies the perturbation of a Lie-Poisson (or, equivalently an Euler-Poincaré) system by a special dissipation term that has Brockett’s double bracket form. We show that a formally unstable equilibrium of the unperturbed system becomes a spectrally and hence nonlinearly unstable equilibrium after the perturbation is added. We also investigate the geometry of this dissipation mechanis...

In this paper we address the constructive controllability problem for drift-free, leftinvariant systems on nite-dimensional Lie groups with fewer controls than state dimension. We consider small ( ) amplitude, low-frequency, periodically time-varying controls and derive average solutions for system behavior. We show how the pth-order average formula can be used to construct open-loop controls f...

We have developed CIRCA, the Cooperative Intelligent Real-time Control Architecture, as a mechanism for automating the on-line, adaptive design of real-time systems. The real-time control tasks generated by CIRCA do not meet many of the simplifying assumptions made to develop traditional scheduling algorithms. We examine several problematic issues that arise in scheduling these automatically-ge...