Symbolic control in probabilistic robotics

(This work is in collaboration with Calin Belta of Boston University.)

In the classical robotic motion planning problem, a specification is given simply as “go from A to B while avoiding obstacles”. In reality, the tasks one would like a robot to do can be significantly more complicated than this. For example, perhaps the robot should either A or B, move through targets sequentially (first A, then B, then C), perform surveillance among different regions (visit A and B infinitely often), or even more complicated statements (Go to A. Don’t go to B unless C or D was visited). Such expressivity can be achieved through the use of temporal logics such as Linear Temporal Logic (LTL) as well as motion description languages. In recent years there has been some success on automatically generating motion plans and control strategies from such specifications (see, e.g., the web page of the HyNeSs lab here at BU).

In real-world applications, we must always deal with some level of uncertainty. This may arise from a variety of sources, including noise in the sensors and actuators or from uncertainty about the environment (due, perhaps, to dynamics changes such as the motion of people). The overarching goal of our work is to achieve a given task in the face of this uncertainty.

We are focusing on specifications given in a temporal logic. Given a specification, we would like to automatically determine the control strategy that maximizes the probability of achieving this specification. To date we have achieved this using statements in PCTL, a probabilistic version of the Computation Tree Logic.

To experimentally validate our approach, we utilize primarily the Robotic InDoor Environment (RIDE). This system utilizes pieces of extruded polystyrene as building blocks, allowing environments of different geometries to be easily constructed. The mobile platform is a iRobot iCreate fitted with a laser range finder, an RFID reader, and a netbook. The RIDE and an iCreate are shown below.

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  1. M. Lahijanian, J. Wasniewski, S.B. Andersson, and C. Belta, “Motion planning and control from temporal logic specifications with probabilistic satisfaction guarantees,” IEEE International Conference on Robotics and Automation, 2010, to appear. download preprint
  2. M. Lahijanian, S.B. Andersson, and C. Belta, “A probabilistic approach for control of a stochastic system from LTL specifications,” IEEE Conference on Decision and Control, pp. 2236-2241, 2009. download