State Estimation for Legged Robots - Consistent Fusion of Leg Kinematics and IMU

This paper introduces a state estimation framework for legged robots that allows estimating the full pose of the robot without making any assumptions about the geometrical structure of its environment. This is achieved by means of an Observability Constrained Extended Kalman Filter that fuses kinematic encoder data with on-board IMU measurements. By including the absolute position of all footholds into the filter state, simple model equations can be formulated which accurately capture the uncertainties associated with the intermittent ground contacts. The resulting filter simultaneously estimates the position of all footholds and the pose of the main body. In the algorithmic formulation, special attention is paid to the consistency of the linearized filter: it maintains the same observability properties as the nonlinear system, which is a prerequisite for accurate state estimation. The presented approach is implemented in simulation and validated experimentally on an actual quadrupedal robot.

[1]  Roland Siegwart,et al.  Starleth: A compliant quadrupedal robot for fast, efficient, and versatile locomotion , 2012 .

[2]  Uluc Saranli,et al.  Model-Based Proprioceptive State Estimation for Spring-Mass Running , 2011, Robotics: Science and Systems.

[3]  Kang G. Shin,et al.  Minimum-time control of robotic manipulators with geometric path constraints , 1985 .

[4]  Jose A. Cobano,et al.  Location of legged robots in outdoor environments , 2008, Robotics Auton. Syst..

[5]  Jean-Jacques E. Slotine,et al.  Improving the Efficiency of Time-Optimal Path-Following Algorithms , 1988, 1988 American Control Conference.

[6]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[7]  Jeffrey K. Uhlmann,et al.  A counter example to the theory of simultaneous localization and map building , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[8]  Daniel E. Koditschek,et al.  Sensor data fusion for body state estimation in a hexapod robot with dynamical gaits , 2006, IEEE Trans. Robotics.

[9]  G. Oriolo,et al.  Robotics: Modelling, Planning and Control , 2008 .

[10]  Matej Hoffmann,et al.  Dead reckoning in a dynamic quadruped robot: Inertial navigation system aided by a legged odometer , 2011, 2011 IEEE International Conference on Robotics and Automation.

[11]  J. Bobrow,et al.  Time-Optimal Control of Robotic Manipulators Along Specified Paths , 1985 .

[12]  Z. Shiller,et al.  Computation of Path Constrained Time Optimal Motions With Dynamic Singularities , 1992 .

[13]  M.Q.-H. Meng,et al.  Localization for Legged Robot with Single Low-Resolution Camera using Genetic Algorithm , 2007, 2007 IEEE International Conference on Integration Technology.

[14]  Heiko Hirschmüller,et al.  Multisensor data fusion for robust pose estimation of a six-legged walking robot , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[15]  Rüdiger Dillmann,et al.  Localization of Walking Robots , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[16]  Daniel D. Lee,et al.  Proprioceptive localilzatilon for a quadrupedal robot on known terrain , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[17]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[18]  Stergios I. Roumeliotis,et al.  Observability-based Rules for Designing Consistent EKF SLAM Estimators , 2010, Int. J. Robotics Res..

[19]  J. C. Hung,et al.  Local observability matrix and its application to observability analyses , 1990, [Proceedings] IECON '90: 16th Annual Conference of IEEE Industrial Electronics Society.

[20]  Mike Stilman,et al.  Turning Paths Into Trajectories Using Parabolic Blends , 2011 .

[21]  Xiaoji Niu,et al.  Analysis and Modeling of Inertial Sensors Using Allan Variance , 2008, IEEE Transactions on Instrumentation and Measurement.

[22]  Surya P. N. Singh,et al.  Optical Flow Aided Motion Estimation for Legged Locomotion , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[23]  Leon Zlajpah,et al.  On time optimal path control of manipulators with bounded joint velocities and torques , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[24]  Friedrich Pfeiffer,et al.  A concept for manipulator trajectory planning , 1987, IEEE J. Robotics Autom..

[25]  Stergios I. Roumeliotis,et al.  Analysis and improvement of the consistency of extended Kalman filter based SLAM , 2008, 2008 IEEE International Conference on Robotics and Automation.

[26]  Daniel E. Koditschek,et al.  A leg configuration measurement system for full-body pose estimates in a hexapod robot , 2005, IEEE Transactions on Robotics.