Advances in Motion Sensing and Control for Robotic Applications: Selected Papers from the Symposium on Mechatronics, Robotics, and Control (SMRC’18)- CSME International Congress 2018, May 27-30, 2018 Toronto, Canada

© Springer Nature Switzerland AG 2019

Farrokh Janabi-Sharifi and William Melek (eds.)Advances in Motion Sensing and Control for Robotic ApplicationsLecture Notes in Mechanical Engineeringhttps://doi.org/10.1007/978-3-030-17369-2_1

Sensor Filtering and State Estimation of a Fast Simulated Planar Bipedal Robot

Stefano Rossi¹   and S. Andrew Gadsden¹  

(1)

College of Engineering and Physical Sciences, University of Guelph, Guelph, ON, Canada

Stefano Rossi (Corresponding author)

Email: [email protected]

S. Andrew Gadsden

Email: [email protected]

Abstract

The development of bipedal humanoid robots is a very prevalent area of research today. Legged robots have many advantages over wheeled robots on rough or uneven terrains. Due to the rapid growth in robotics, it is unavoidable that legged robots will be adapted for everyday household settings. However, the agile bipedal robots possesses many design and control challenges. Model based control of humanoid robots relies on the accuracy of the state estimation of the model’s constituents. The spring loaded inverted pendulum (SLIP) is frequently used as a fundamental model to analyze bipedal locomotion. In general, it consists of a stance phase and a flight phase, employing different strategies during these phases to control speed and orientation. Due to the underactuation and hybrid dynamics of bipedal robots during running, estimating the state of the robot’s appendages can be challenging. In this paper, various Kalman estimation techniques are combined with sensor data fusion to predict the spatial state of a fast simulated planar SLIP model.

Keywords

State estimationBipedal robotKalman filter

1 Introduction

Unlike fixed based robots, bipedal robots have a floating base and are high degree of freedom dynamical systems. They can move around complex environments and state estimation is a crucial part of controlling such a system. For a controller using the model dynamics to compute feed-forward torques, the state estimator needs to provide the orientation, linear and angular velocities of each component.

The introduction of accurate full body state estimates as well as force interactions with the external environment throughout the phases of rapid locomotion considerably increases the agility of legged robots [1]. Empirical studies of proprioception controllers relying on inertial measurement unit (IMU) feedback has resulted in significantly improved performance of legged robots [2]. Performance improved on varying terrain such as slopes and broken terrain [3], as well as introducing entirely new behaviors such as flips [4] and unique gaits [5]. In mobile robotics, the concept of sensor data fusion has already been widely used on wheeled vehicles. However, in the field of legged robotics, there has only been limited study in applying sensor fusion to control robot behavior. The implementation of a cost effective sensor suite to deliver full body state estimation relevant to motor control remains a challenge in legged locomotion, due to the severe drift and sensitivity of low cost IMU packages. While sensor fusion has been applied to the estimation and control of walking bipedal robots [6], it has yet to be tested on a biped undergoing rapid locomotion.

In this paper the effectiveness of state estimation of a rapid biped robot using common IMU sensors will be tested in a simulated environment. Various methods of integrating and filtering these sensors will be explored with the goal of providing a basis for cost effective alternatives in researching rapid bipedal locomotion control. Research in the development of agile bipedal robotics is rapidly growing, yet state estimation remains difficult due to the hybrid dynamics and non-linearity inherit to rapid locomotion [7]. The aim of this experiment is to demonstrate that accurate state estimation of rapid locomotion robots can be done utilizing simple models and cost effective sensor data fusion as opposed to closed form motion planning.

An overview of the background and previous works related to rapid locomotion will be outlined. A framework of the design goals for a sensor based state estimator will be extrapolated from previous works, as well as a description of the methods and model to be used.

2 Background and Previous Work

2.1 Sensory Pose Estimation of Legged Robots

Due to the rapid development of modern legged robots, the underlying principles of dynamically stable locomotion have been revealed. As a result, more research is being done on how to increase a robot’s performance and agility through sensory feedback and data fusion algorithms.

One of the earliest attempts [8] of estimating a legged robot’s global pose was performed on a hexapod robot, the Ambler. The position of the feet was calculated from the motor input commands and encoder measurements on the joints. More recently, pose estimation techniques for a hexapod were developed by fusing IMU data, vision and leg odometry [8]. Regarding dynamical gaits, an extended Kalman filter (EKF) based body estimation approach only using proprioceptive sensors and leg kinematics was introduced in a hexapod [9]. With regards to biped robots, sensor fusion utilizing observer based data and preview control has be utilized for stabilizing walking motion on a 3 dimensional linear inverted pendulum model [10]. The use of only proprioceptive sensor fusion has been applied to bipedal robots and feedback control applications, but only in the context of stable walking and turning [6], and not yet to rapid locomotion.

Based on an assessment of the previous works, it is conjectured that a suitable filter for general biped estimation should (1) only use proprioceptive sensors (2) make no assumptions about the outside environment or gait and (3) be easily adaptable to any general rapid bipedal locomotion platform.

2.2 Estimation Framework

The Kalman Filter (KF) is an optimal state estimation strategy, and is widely used in the field of control and estimation theory [11–14]. The Kalman filter provides an estimate of the state along with a corresponding covariance matrix which outlines the uncertainty of the estimate. The Kalman filter involves two steps, the prediction step where the previous state estimates are propagated through the system to produce a priori estimates, and the update step where the a priori estimates are combined with the current observed measurements to refine the state estimate, referred to as the a posteriori state estimate.

2.3 SLIP Model

To study running in its simplest form, a single legged planar running machine was built [15] in 1984, to be later recognized as the Spring Loaded Inverted Pendulum model (SLIP model). Although the robot only had one leg, the main principle is identical to a biped, and the SLIP model is widely used today to study dynamically stable running. The original machine used a pneumatic leg simulate a telescopic passive spring and was capable of exerting a thrust force. A single running cycle consists of a stance and flight phase. During the stance phase, the leg supports the body and remains in a fixed position on the ground. In this phase, the robot tips like an inverted pendulum while the spring undergoes compression and then thrust. During stance, there is no chance to move the foot placement to control position. In order to change the foot position, the robot jumps to flight phase where the leg is unloaded and free to swing. Marc Raibert developed a simple control strategy for simple legged robots which allowed them to perform dynamically stable running, as well as regulate speed and body attitude. This control method relied on measurements of the forward speed and body attitude [16].

3 Simulated Model

The model used in this paper was created in VREP and modelled after the Raibert planar biped [17]. The model consists a rectangular main body, with two actuated hip joints, which connect to telescopic legs (Fig. 1). The leg acts as a passive spring/damper during the compression portion of the stance phase, and are capable of applying a thrust force. The robot is attached to a spherical joint at the hip by a 5 m massless boom. This eliminates 3DOF from the model, its yaw, roll and lateral movement. The feet consist of spheres and have perfect friction with the ground (μ = 1) (Table 1).

Fig. 1

Simulated biped model assembly

Table 1

Symbols and descriptions

The simulation used Open Dynamics Engine as its physics engine due to its accuracy modelling spring damper systems. The main control loop is implemented directly in VREP via a child script. The running motion of the robot can be described in 5 phases: flight, touchdown, compression, thrust and takeoff. The main working principle behind the speed control is foot placement. Because the leg acts as a spring-damper, the time of the stance phase (compression and thrust) can be approximated by:

(1)

Foot placement has a direct effect on the resultant velocity at takeoff (Fig. 2). If the foot is placed directly at the halfway point throughout the stance (neutral point), the stance phase is symmetric and the takeoff velocity is the same as the touchdown.

(2)

Fig. 2

Free body diagram (right) and illustration of how touchdown foot placement effects the takeoff trajectory (left)

Any deviation from the neutral point results in a non-zero horizontal acceleration. Placing the foot before the neutral point results in positive acceleration in the forward direction, as more of the vertical velocity is converted to horizontal, and vice versa (Fig. 2). Therefore, foot position on touchdown is used accelerate to a desired speed. This is regulated by proportional control. The algorithms for foot placement and corresponding hip angles are:

(3)

(4)

Body attitude is maintained by applying a torque about the hip during the stance phase. Since angular momentum is conserved during flight, the friction between the foot and the ground provides an opportunity to correct the angular momentum of the entire system. To servo the body to a desired attitude, the control torque is applied