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A constraint-based approach for computing fault tolerant robot programs Ralph, Scott

Abstract

We develop a new framework, based on the Least Constraint, for programming robots to perform a task using a fault tolerant trajectory. We take a specification of the task, expressed as a set of constraints on the robot's configuration over time, and produce a fault tolerant trajectory. The methodology encourages fault tolerant behavior at two levels: first at the task-design phase by encouraging the designer to omit extraneous constraints which reduce the potential for fault tolerant operation, and secondly, at the trajectory generation phase by avoiding critical configurations. The critical configurations are identified via a measure of fault tolerance which is global in nature. The dual optimization of fault tolerance at both the high-level design phase as well as the low-level recoverymotion generation phase allows more of the inherent fault tolerance of the robot to be exploited. We believe that combining these two processes into a single formalism is unique and beneficial. The methodology is unique in its ability to deal with robots which are not kinematically redundant with respect to arbitrary task, but which are sufficiently redundant with respect to the particular task constraints to allow the task to be described as a set of "loose" constraints over time. The constraint-based approach allows us to model faults as additional constraints to the specification, thereby allowing an efficient means of computing the effect a fault will have on the ability to complete the task, using the reduced configuration space of the robot. Faults not previously considered, such as the inclusion of additional obstacles, as well as dynamic information arising from sensors, can also be included using this formalism. An efficient algorithm for constructing a recovery motion for a fault has been developed. A specific example of a seldom considered fault, the collision of the robot with an unknown obstacle, is presented. We show that in addition to detecting the event, we are also able to recover the collision geometry. This information can then be used in a more intelligent recovery motion selection. We have developed a new global fault tolerance measure called longevity. The fault tolerance measure examines a set of faults which may occur at a given configuration, and based on the optimal recovery motions for the given fault, ranks the configuration in its ability to satisfy the future task requirements. Using this fault tolerance measure, a trajectory which maximizes the worst-case failure mode of the robot is computed. A number of experiments show the applicability of the method to a number of domains. We analyze the resulting trajectories with respect to their ability to sustain a fault, and we compare them to more traditional methods for accomplishing the same task. We demonstrate that trajectories obtained using the least constraint specification and the fault tolerance measure are able to achieve a much larger degree of fault tolerance than naive methods for the same task. The fault tolerant trajectories make optimal use of the 1-fault tolerant configuration space, and maximize the worst-case utility of the trajectory given a fault.

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