A Computational Feasibility Study of Failure-Tolerant Path Planning Rodrigo S. Jamisola, Jr. † , Anthony A. Maciejewski † , & Rodney G. Roberts ‡ † Colorado State University, Ft. Collins, Colorado 80523-1373, USA ‡ Florida A&M-Florida State University, Tallahassee, Florida 32310-6046, USA E-mails: r.jamisola@colostate.edu, aam@colostate.edu, & rroberts@wombat.eng.fsu.edu Abstract— This work considers the computational costs associated with the implementation of a failure-tolerant path planning algorithm proposed in [1]. The algorithm makes the following assumptions: a manipulator is redundant relative to its task, only a single joint failure occurs at any given time, the manipulator is capable of detecting a joint failure and immediately locks the failed joint, and the environment is static and known. The algorithm is evaluated on a three degree-of-freedom planar manipulator for a total of eleven thousand different scenarios, randomly varying the robot’s start and goal positions and the number and locations of obstacles in the environment. Statistical data are presented related to the computation time required by the different steps of the algorithm as a function of the complexity of the environment. I. I NTRODUCTION Kinematic failure tolerance gives a robot the ability to gracefully recover from joint failures. Such a control strategy is most useful for robots performing tasks in hazardous or remote environments, such as in space ex- ploration [2], [3], underwater exploration [4], and nuclear waste disposal [5], [6], [7]. It allows a robot to imme- diately complete the task at hand without unnecessary delays due to robot repair and also avoid the potentially significant danger associated with a robot failure during task execution amongst hazardous materials. A worst-case failure-tolerance measure was first intro- duced in [8] using the minimum singular value of the robot Jacobian matrix. The nature of joint failures that have been studied include locked-joint [9], [10], [11] and free- swinging [12] joint failures. A real-time implementation is given in [11]. A number of failure-tolerant control strategies have been proposed, including adaptive control [13], [14], [15], reflex control [16], and least squares approaches [17]. Generally, obstacles are not considered in most kinematic failure tolerance studies. One of the earliest works in kinematic failure tolerance that does consider obstacles in the workspace is [18]. However, the method introduced extensively checks every possibility of failure at every instance in time as the robot plans to move from a start to a goal workspace location. In more recent work [1], a method was introduced that guarantees task completion for any single locked-joint failures despite obstacles in the workspace without extensively checking every possibility of failure at every instance in time. The approach searches for a continuous obstacle-free mono- tonic surface in the configuration space that guarantees the existence of a solution. The goal of this work is to quantify the computational feasibility of implementing the kinematic failure tolerance algorithm presented in [1]. We first provide a review of this approach. This is followed by a set of simula- tion experiments consisting of eleven thousand scenarios, where a scenario is defined as a workspace start location, a workspace goal location, and a set of obstacles. The resulting data is then analyzed to determine the types of scenarios where the implementation of a failure-tolerant path planning strategy may be feasible. II. DEFINITION OF TERMS For an n degree-of-freedom (DOF) kinematically re- dundant robot operating in an m DOF workspace, the degree-of-redundancy (DOR) is defined as r = n - m. The set of configurations in the configuration space (C- space) that result in the same end-effector workspace position/orientation x is called the pre-image of x, denoted f -1 (x). The pre-image can be written as a union of disjoint connected sets f -1 (x)= nm  i=1 M i (1) where M i is the i-th r-dimensional self-motion manifold in the inverse kinematic pre-image such that M i ∩ M j = ∅ when i = j , and n m is the number of self-motion manifolds [19]. Fig. 1 shows a set of single dimensional start and goal self-motion manifolds for a robot with r =1. The dark portions of the self-motion manifolds denote configurations of the robot that are in contact with obstacles. A continuous obstacle-free portion of the goal self-motion manifold is denoted as γ g while an obstacle- free start configuration is denoted as θ s . For a single locked-joint failure, the resulting C-space is an (n - 1)-dimensional hyperplane called a failure hyperplane. For an obstacle-free start configuration θ s , 10th Robotics & Remote Systems Mtg. Proceedings, Gainesville, Florida - March 28-31, 2004 233