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

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.Copyright © 2007 by ASME

[1]  Moshe Shoham,et al.  Singularity condition of six-degree-of-freedom three-legged parallel robots based on grassmann-cayley algebra , 2006, IEEE Transactions on Robotics.

[2]  Jeremy Rex Heaston.  Design of a Novel Tripedal Locomotion Robot and Simulation of a Dynamic Gait for a Single Step , 2006 .

[3]  Ping Ren,et al.  Novel Tripedal Mobile Robot and Considerations for Gait Planning Strategies Based on Kinematics , 2007 .

[4]  Dennis Hong,et al.  Biologically Inspired Locomotion Strategies: Novel Ground Mobile Robots at RoMeLa , 2006 .

[5]  Leila Notash,et al.  Complete forward displacement solutions for a class of three-branch parallel manipulators , 1994, J. Field Robotics.

[6]  Ron P. Podhorodeski,et al.  A class of parallel manipulators based on kinematically simple branches , 1994 .

[7]  Mark W. Spong,et al.  Robot dynamics and control , 1989 .

[8]  Raymond J. Cipra,et al.  Optimal Contact Force Distribution for Multi-Limbed Robots , 2006 .

[9]  Ping Ren,et al.  STriDER: Self-Excited Tripedal Dynamic Experimental Robot , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[10]  Dennis Hong,et al.  Design Optimization of a Novel Tripedal Locomotion Robot Through Simulation and Experiments for a Single Step Dynamic Gait , 2007 .

[11]  Tad McGeer,et al.  Passive Dynamic Walking , 1990, Int. J. Robotics Res..

[12]  Leila Notash,et al.  On the forward displacement problem of three-branch parallel manipulators , 1995 .

[13]  Raymond J. Cipra,et al.  Visualization of the Contact Force Solution Space for Multi-Limbed Robots , 2006 .

[14]  Mark W. Spong,et al.  Further results on control of the compass gait biped , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[15]  Dennis Hong,et al.  Synthesis of the Body Swing Rotator Joint Aligning Mechanism for the Abductor Joint of a Novel Tripedal Locomotion Robot , 2007 .

[16]  Carlo Innocenti,et al.  Direct position analysis of the Stewart platform mechanism , 1990 .

[17]  H. Sebastian Seung,et al.  Actuating a simple 3D passive dynamic walker , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.