Keywords: Deception, Robotics, Probability Theory, HRI, Markov Process
Most of the robotics research has been done on effective communication of true information     . There is a natural counterpart of effective communication: deception, which imparts wrong information or just conceals it completely. Deception has a long history related to the study of intelligent systems. According to biologists and psychologists, deception provides an evolutionary advantage for the deceiver . Higher-level primates also depict deception which serves as an indicator of the theory of mind .
Animals use different types of deception mechanisms and they are, either intentional or unintentional, necessary for their survival. As an example, a grasshopper uses camouflage to deceive predators. Camouflage and mimicry are examples of unintentional deception but, there are some animals which deceive in a seemingly more intentional way. For example , chimpanzees deceive in different ways based on the situation and their objectives. According to an observation, a chimpanzee once faked having its arm stuck in the bars of its cage in order to lure the zookeeper nearby. Once he came closer to help it, the chimpanzee jumped onto the zookeeper. Animals like squirrels or hamsters use a different type of deceptive strategy for food hoarding .
Robots can also gain an advantage over rivals by practicing deceptive behavior. For example, it is quite obvious that robot deception has applications in the military  . Sun Tzu stated in The Art of War
, “All warfare is based on deception”. Robots are the future of the military  and robotic deception can provide many new advantages. In other areas, like education, a deceptive teacher can help improve students’ learning efficiency. At University of Tsukuba,  Tanaka and his team developed an experimental setup where they demonstrated that a deceptive robot partner can improve the learning efficiency of children. The goal of that learning game was for children to draw shapes of corresponding English words, like a circle or a square etc. The robot partner acted as a teacher and made some mistakes deliberately. According to the results, the deceptive dumb behavior of the robot increased the learning efficiency of the students. . Moreover, in healthcare, deceptive robots can be of great value. For example, to help patients recover from an injury faster by showing deceptive results .
Although deception has plenty of potential benefits, not a lot of work has been done on deceptive robots. Floreano’s research group  showed that robots evolve to develop deceptive strategies to protect energy sources. Researchers at Georgia Tech have been working in deceptive robotics for a long time and have published studies on different applications of robotic deception. Shim and Arkin wrote the first paper on the taxonomy of robot deception . Arkin provided the viewpoint on current research going on at Georgia Tech in . Three different areas are reviewed in this technical report including: (1) Use of interdependence theory and game theory to let a robot decide both when and how to deceive ; (2) deception in squirrel hoarding as means for deceiving a predator regarding hidden resources ; (3) Use of Grafen’s dishonesty model  in the context of bird mobbing behavior  which is valuable in military situations. Deception via motion channel is a new topic and researchers at Carnegie Mellon University have recently presented their findings in this field .
This paper investigates the use of deception by autonomous mobile robots. Particularly, the purpose of this research is to develop and investigate an algorithm, for a mobile robot, that can deceive humans in a long run i.e. even if the humans have seen all the possible trajectories, the algorithm should still be able to deceive them. The paper has two parts: 1) Implement the mathematical model, presented in , on an autonomous mobile robot simulator and generate the three main deceptive trajectories (Exaggerating, Switching, and Ambiguous), 2) Develop an algorithm to use the deceptive trajectories, in , to deceive humans in a long run.
In the remainder of this paper, we first summarize some relevant research. Then, we used probability theory to develop an algorithm to deceive humans using available trajectories. Finally, we present user studies to test the deceptive strategies on a mobile robot simulator and investigate the effectiveness of our adaptive long run algorithm. The paper is concluded with a discussion of the user studies and some directions for future research.
II. RELATED WORK
Much of the current research in robot deception focuses on applications and not on the fundamental theory. Shim and Arkin presented a foundation for the field of robot deception formalizing the definition of a taxonomy for this field . They presented eight types of robot deception based on the type of the subject the robot is trying to deceive (human (H) or non-human (N)); which of the two: deceiver (S) and deceived (O), will benefit from the situation; and if the deception is intentional (B) or unintentional (P). This paper focuses on the category H-S-B: “Deceiving humans for deceiver robot’s own benefit using behavioral interactions”.
After defining the type of our focus of research in robot deception, we analyzed papers on deceptive robot motion in the category H-S-B, particularly the work done by researchers at Carnegie Mellon University in this field  . Anca Dragan and her team discussed different deceptive motion trajectories in the case of a two target system and studied the deceptive effects of those trajectories on human participants . They used a 2 Degree Of Freedom (DOF) arm robot for their experiments and performed different studies based on the deceptive trajectories generated by the robotic arm in a two-target system. They first started by analyzing how humans would deceive in an environment when two targets are available and they have to choose one of them in a deceptive manner. After their analysis they came up with three main deceptive trajectories: Exaggerating, Switching and Ambiguous (See Figure 1).
(a) Exaggerating (b) Switching (c) Ambiguous
Figure 1. Three main deceptive trajectories. The trajectories in gray show the optimization trace, starting from the predictable trajectory 
They developed a mathematical model and came up with following three equations for the three trajectories, shown in Figure 1.
The mathematical model for exaggerating trajectory translated into maximizing the probability
and M.H. Overmars, "Probabilistic roadmaps for path planning in high-dimensional configuration spaces," IEEE Transactions on Robotics and Automation,
vol. 12, no. 4, pp. 566-580, August 1996.
A. Papoulis and S. Pillai, Probability, Random Variables and Stochastic Processes, 4th Edition, McGraw Hill, 2002.
W. W. Claude E Shannon, The Mathematical Theory of Communication, University of Illinois Press, Sep 1, 1998.
X. H. M. K. N. T.-K. S. Wai-Ki Ching, "Higher-Order Markov Chains," in Markov Chains
, Springer US, 2013, pp. 141-176.
Ali Ayub, Aldo Morales and Amit Banerjee, "An Analysis of the Adapive Long-Run Deception Algorithm," In Progress.
R. Likert, "A Technique for the Measurement of Attitudes," Archives of Psychology,
vol. 140, pp. 1-55, 1932.