Forward and Inverse Displacement Analysis of a Novel Three-Legged Mobile Robot Based on the Kinematics of In-Parallel Manipulators

Abstract

This paper presents the forward and inverse displacement analysis of a novel three-legged walking robot STriDER (Self-excited Tripedal Dynamic Experimental Robot). STriDER utilizes the concept of passive dynamic locomotion to walk, but when all three feet of the robot are on the ground, the kinematic structure of the robot behaves like an in-parallel manipulator. To plan and control its change of posture, the kinematics of its forward and inverse displacement must be analyzed. First, the concept of this novel walking robot and its unique tripedal gait is discussed including strategies for changing directions, followed by the overall kinematic configuration and definitions of its coordinate frames. When all three feet of the robot are on the ground, by assuming there are no slipping at the feet, each foot contact point are treated as a spherical joint. Kinematic analysis methods for in-parallel manipulators are briefly reviewed and adopted for the forward and inverse displacement analysis for this mobile robot. Both loop-closure equations based on geometric constraints and the intersection of the loci of the feet are utilized to solve the forward displacement problem. Closed-form solutions are identified and discussed in the cases of redundant sensing with displacement information from nine, eight and seven joint angle sensors. For the non redundant sensing case using information from six joint angle sensors, it is shown that closed-form solutions can only be obtained when the displacement information is available from non-equally distributed joint angle sensors among the three legs. As for the case when joint angle sensors are equally distributed among the three legs, it will result in a 16th-order polynomial of a single variable. Finally, results from the simulations are presented for both inverse displacement analysis and the non redundant sensing case with equally distributed joint angle sensors. It was found that at most sixteen forward displacement solutions exist if displacement information from two joint angle sensors per leg are used and one is not used.