Professor Cheatham's research is concerned with space and medical applications of advanced robotics systems. In particular, he is conducting research on applications of artificial intelligence aimed at making robots more autonomous.

Professor Cheatham and his research group are investigating artificial neural networks and fuzzy logic for use in the control of hyperredundant manipulator arms, and they are studying genetic algorithms as a way of optimizing fuzzy membership functions. They have developed a fuzzy camera tracking system and are evaluating a stereo version.

Design teams under Professor Cheatham's supervision and in collaboration with electrical engineering faculty, staff, and students have built a prototype of a myoelectric prosthetic hand. The support group for this project includes personnel from the Limbs of Love Foundation, Muilenburg Prosthetics, Inc., Baylor College of Medicine, The Institute for Rehabilitation and Research, NASA's Johnson Space Center, Oceaneering Space System, and McDonnell Douglas Space Systems. A second generation prosthesis is currently being developed.

Professor Cheatham is a Fellow of the American Society of Mechanical Engineers and received the ASME's Ralph James Award in 1981. He was named a Distinguished Author of the Society of Petroleum Engineers in 1984.