This paper presents a generalized method of determining the static shape conformation of a cable-driven serpentine robot. Given a set of desired cable displacements as model inputs, the model calculates the joint angles and cable tensions that result from those displacements. The model’s governing equations are derived from ensuring static equilibrium at each of the robot’s revolute joints, along with compatibility equations ensuring the joint angles result in the desired cable displacements. Elastic, actuation and gravitational loading are included in the model, and the results analyze the relative impact of each for various combinations of cable displacement inputs. In addition, the impact of elasticity and mass distribution on the accuracy of purely kinematic constant-curvature segment models is presented. In addition, the model also accommodates limits for the serpentine joint angles. The model is implemented in MATLAB, and results are generated to analyze the impact of the actuation, elastic and gravitational effects. Future work will include inertial effects in the model to make it dynamic. These models will be used as the foundation for a serpentine tail design for use on-board a mobile robot, and for task planning to enable that tail to be effectively used in various scenarios.

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