Robot’s Velocity and Tilt Estimation Through Computationally Efficient Fusion of Proprioceptive Sensors Readouts Pawel Wawrzy´ nski, Member, IEEE Institute of Control and Computation Engineering Warsaw University of Technology 00-665 Warsaw, Poland, p.wawrzynski@elka.pw.edu.pl Abstract— In this paper a method is introduced that combines Inertial Measurement Unit (IMU) readouts with low accuracy and temporarily unavailable velocity measurements (e.g., based on kinematics or GPS) to produce high accuracy estimates of velocity and orientation with respect to gravity. The method is computationally cheap enough to be readily implementable in sensors. The main area of application of the introduced method is mobile robotics. Keywords—velocity estimation, Kalman filter, mobile robotics. I. I NTRODUCTION Knowledge of velocity of a robot or its specific part is usually crucial for their efficient control. Orientation of the robot with respect to gravity vector is important especially in legged robots, where it enables balancing of their body. Velocity estimation is possible with a system based on vision [1] or Global Positioning System (GPS) [2], [3], [4]. However, in many applications where autonomy of the robot is required, exteroceptive sensors are unwanted. It is known that velocity and orientation may be estimated by proper integration of Inertial Measurement Unit (IMU) readouts. However, IMU can not be used alone, as it is prone to the so-called ’drift’ effect which makes the estimates practically useless [5]. In [6] we proposed a method that combines IMU readouts with velocity measurements that come from robot kinematics to produce velocity and orientation estimates of a legged robot. The estimates are generally of high accuracy even if measurements are of low accuracy and are temporarily unavailable. In this paper we present a version of this method that is so computationally inexpensive that it may be in principle implemented on electronics within a sensor (e.g., IMU). The structure of this paper is as follows: Sec. II presents the formal problem definition, and the notation used throughout the paper. In Sec. III basic tools for the velocity estimation are presented along with Extended Kalman Filter sensor fusion. Sec. IV introduces the contribution of this paper, which is a computationally inexpensive filter for velocity estimation. Experimental data analysis and discussions are given in Sec. V. Finally, in Sec. VI a brief summary of the results is given. II. PROBLEM FORMULATION A point in the robot body is given with Inertial Measurement Unit (IMU) attached to it. IMU measures acceleration and angular velocity. An auxiliary sensor measures velocity of IMU in a drift-less manner. This auxiliary measurement may result from leg’s kinematics, angular velocity of wheels, or GPS. It may be temporarily unavailable because of no leg touching the ground, inaccessibility of GPS satellites, and so on. At each moment we wish accurate measurement of velocity and tilt of IMU in the frame in which this sensor takes measurements. This frame, hereafter called IMU frame is immobile with respect to the ground and at each moment it is parallel to IMU. Tilt is expressed as gravity vector in IMU frame. It is understood that having velocity and tilt in IMU frame, we are able to express velocity and orientation of IMU in any coordinate system. We are not able to express global yaw, but without external reference point we are not able to estimate it with high accuracy anyway. We require that velocity and tilt estimates are recursive, and their update on the basis of coming data are based on limited computational effort. In essence, we require that the whole computational burden may be handled by a microprocessor within IMU. Notation Whenever it matters, we assume right-hand coordinate sys- tem and right-wise rotations for positive angle. We also apply the following notation conventions. a ∈ R 3 is an acceleration vector measured by IMU, i.e., a sum of linear acceleration and acceleration due to gravity, in IMU frame. ω ∈ R 3 is the angular velocity of IMU in IMU frame. g ∈ R 3 is the gravity vector in IMU frame. v ∈ R 3 is the velocity vector of IMU in IMU frame. δ is the constant time elapsing between consecutive IMU measurements. 738 978-1-4799-8701-6/15/$31.00 ©2015 IEEE.