From Discrete Task Plans to Continuous Trajectories

We present a logic-based framework to provide robots with high-level reasoning, such as planning. This framework uses the action description language C+ to represent actions and changes, and the system CCALC to reason about them. In particular, we can represent action domains that involve concurrent actions and additive fluents; based on this description, we can compute shortest plans to a planning problem that involves cost constraints. We show the applicability of this framework on two LEGO MINDSTORMS NXT robots: we compute a discrete task plan (possibly with concurrency) with a cost less than a specified value, and transform this plan into a continuous collision-free trajectory. Introduction There have been various studies to close the gap between traditional robotics and cognitive robotics (Levesque and Lakemeyer 2007), by implementing high-level robot control systems based on different families of formalisms for reasoning about actions and change. For instance, (Levesque and Pagnucco 2000) describes a system, LEGOLOG1, that controls a LEGO MINDSTORMS RIS robot using the highlevel control language GOLOG (Levesque et al. 1997) based on the situation calculus (McCarthy 1963; Levesque, Pirri, and Reiter 1998). (Hähnel, Burgard, and Lakemeyer 1998) presents an execution monitoring system for GOLOG and the RHINO control software which operates on RWI B21 and B14 mobile robots. (Ferrein, Fritz, and Lakemeyer 2005) studies coordination of soccer playing robots, using an extension of GOLOG. In the WITAS Unmanned Aerial Vehicle Project2 temporal action logic (Doherty et al. 1998), features and fluents (Sandewall 1994), and cognitive robotics logic (Sandewall 1998) are used for representing the actions and the events, as a part of a helicopter control system (Doherty et al. 2000). (Shanahan and Witkowski 2000) describes how event calculus (Kowalski and Sergot 1986; Miller and Shanahan 1999) can be used to provide high-level control for a Khepera robot. The agent programming language FLUX (Thielscher 2005), based on the fluent calculus (Thielscher 1998), has also been used to control the execution of some robots.3 For instance, (Fichtner, Großmann, http://www.cs.toronto.edu/cogrobo/Legolog http://www.ida.liu.se/ext/witas http://www.fluxagent.org/projects.htm Execute the plan Compute a plan Action Domain Description (formalized in C+) Planning Problem