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Robot systems in critical applications, such as those in space and nuclear environments, must be able to operate during component failure to complete important tasks. One failure mode that has received little attention is the failure of joint position sensors. Current fault tolerant designs require the addition of directly redundant position sensors which can affect joint design. The proposed method uses joint torque sensors found in most existing advanced robot designs along with easily locatable, lightweight accelerometers to provide a joint position sensor fault recovery mode. This mode uses the torque sensors along with a virtual passive control law for stability and accelerometers for joint position information. Two methods for conversion from Cartesian acceleration to joint position based on robot kinematics, not integration, are presented. The fault tolerant control method was tested on several joints of a laboratory robot. The controllers performed well with noisy, biased data and a model with uncertain parameters.