Full paper Reliability Maps for Probabilistic Guarantees of Task Motion for Robotic Manipulators Hamid Abdi a *, Anthony A. Maciejewski b and Saeid Nahavandi a 5 a Centre for Intelligent Systems Research, Deakin University, Waurn Ponds Campus, Victoria 3217, Australia; b Electrical and Computer Engineering Department, Colorado State University, Fort Collins, CO 80523, USA Received 25 November 2011; accepted 2 March 2012 Abstract 10 There are many applications for which reliable and safe robots are desired. For example, assistant robots for disabled or elderly people and surgical robots are required to be safe and reliable to prevent human injury and task failure. However, different levels of safety and reliability are required for different tasks so that understanding the reliability of robots is paramount. Currently, it is possible to guarantee the com- pletion of a task when the robot is fault tolerant and the task remains in the fault-tolerant workspace 15 (FTW). The traditional definition of FTW does not consider different reliabilities for the robotic manipulator’ s different joints. The aim of this paper is to extend the concept of a FTW to address the reli- ability of different joints. Such an extension can offer a wider FTW while maintaining the required level of reliability. This is achieved by associating a probability with every part of the workspace to extend the FTW. As a result, reliable fault-tolerant workspaces (RFTWs) are introduced by using the novel concept 20 of conditional reliability maps. Such a RFTW can be used to improve the performance of assistant robots while providing the confidence that the robot remains reliable for completion of its assigned tasks. Ó 2012 Taylor & Francis and The Robotics Society of Japan Keywords fault tolerant robots, workspace analysis, reliability, assistive robots, redundant robots 25 1. Introduction Robots are increasingly applied for more advanced and complex tasks in various applications. This requires further study to improve their performance. For exam- ple, assistant robots have been designed for helping disabled or elderly people 30 [1,2]. These robots are required to be safe and reliable to prevent human injury and task failure. In some tasks, if the robot is unable to accomplish the tasks, then there will be the possibility of serious human injury. Furthermore, safety * To whom correspondence should be addressed. E-mail: hamid.abdi@deakin.edu.au Ó 2012 Taylor & Francis and The Robotics Society of Japan DOI: 10.1080/01691864.2012.703302 TADR CE: SL QA: DS 703302 3 July 2012 Initial Advanced Robotics XX (2012) XXX–XXX tandfonline.com/tadr