Solution for the Direct Kinematics Problem of the General Stewart-Gough Platform by Using only Linear Actuators' Orientations

In this paper, we present a solution for the direct kinematics problem of the general Stewart-Gough platform where only the orientations of the linear actuators are measured with accelerometer sensors. By using an extended Kalman filter with the inverse kinematics equations, we can uniquely determine the manipulator platform’s pose. In this context, we investigate the solution’s accuracy and derive the minimum number of iterations under static conditions and validate our concept with experiments on a state-of-the-art Stewart-Gough platform.

[1]  C. Gosselin Parallel Computational Algorithms for the Kinematics and Dynamics of Planar and Spatial Parallel Manipulators , 1996 .

[2]  Jorge Angeles,et al.  The decoupling of the direct kinematics of parallel manipulators using redundant sensors , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[3]  Jizhong Xiao,et al.  Keeping a Good Attitude: A Quaternion-Based Orientation Filter for IMUs and MARGs , 2015, Sensors.

[4]  Stefan Schulz,et al.  On the Direct Kinematics Problem of Parallel Mechanisms , 2018, J. Robotics.

[5]  Jean-Pierre Merlet,et al.  Closed-form resolution of the direct kinematics of parallel manipulators using extra sensors data , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[6]  Tatsuo Arai,et al.  Optimal sensor placement for forward kinematics evaluation of a 6-DOF parallel link manipulator , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[7]  K. H. Hunt,et al.  Assembly configurations of some in-parallel-actuated manipulators , 1993 .

[8]  Daniel Schreiber,et al.  Sensor concept for solving the direct kinematics problem of the Stewart-Gough platform , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[9]  Stergios I. Roumeliotis,et al.  Determining the robot-to-robot 3D relative pose using combinations of range and bearing measurements: 14 minimal problems and closed-form solutions to three of them , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[10]  Ming-Hwei Perng,et al.  Forward Kinematics of a General Fully Parallel Manipulator with Auxiliary Sensors , 2001, Int. J. Robotics Res..

[11]  Bernard Mourrain,et al.  The 40 “generic” positions of a parallel robot , 1993, ISSAC '93.

[12]  M. Raghavan The Stewart platform of general geometry has 40 configurations , 1993 .

[13]  Yasuyuki Funahashi,et al.  A new analytical system applying 6 DOF parallel link manipulator for evaluating motion sensation , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[14]  Jean-Pierre Merlet,et al.  Solving the Forward Kinematics of a Gough-Type Parallel Manipulator with Interval Analysis , 2004, Int. J. Robotics Res..

[15]  Vincenzo Parenti Castelli,et al.  Accurate and fast body pose estimation by three point position data , 2007 .