Omni-directional mobile robot controller based on trajectory linearization

Abstract

In this paper, a nonlinear controller design for an omni-directional mobile robot is presented. The robot controller consists of an outer-loop (kinematics) controller and an inner-loop (dynamics) controller, which are both designed using the Trajectory Linearization Control (TLC) method based on a nonlinear robot dynamic model. The TLC controller design combines a nonlinear dynamic inversion and a linear time-varying regulator in a novel way, thereby achieving robust stability and performance along the trajectory without interpolating controller gains. A sensor fusion method, which combines the onboard sensor and the vision system data, is employed to provide accurate and reliable robot position and orientation measurements, thereby reducing the wheel slippage induced tracking error. A time-varying command filter is employed to reshape an abrupt command trajectory for control saturation avoidance. The real-time hardware-in-the-loop (HIL) test results show that with a set of fixed controller design parameters, the TLC robot controller is able to follow a large class of 3-degrees-of-freedom (3DOF) trajectory commands accurately.

Introduction

An omni-directional mobile robot is a type of holonomic robots. It has the ability to move simultaneously and independently in translation and rotation. The inherent agility of the omni-directional mobile robot makes it widely studied for dynamic environmental applications [1], [2], [15]. The annual international Robocup competition in which teams of autonomous robots compete in soccer-like games, is an example where the omni-directional mobile robot is used.

The Ohio University (OU) Robocup Team’s entry Robocat is for the Robocup small-size league competition. The current OU Robocup robots are Phase V omni-directional mobile robots, as shown in Fig. 1. The Phase V Robocat has three omni-directional wheels, arranged 120 deg apart. Each wheel is driven by a DC motor installed with an optical shaft encoder. An overhead camera above the field of play senses the position and the orientation of the robots using a real-time image processing algorithm and the data are transmitted to the robot through an unreliable wireless communication channel.

A precise trajectory tracking control is a key component for applications of omni-directional robots. The trajectory tracking control of an omni-directional mobile robot can be divided into two tasks, path planning and trajectory following [3], [5]. Path planning calls for computing a feasible and optimal geometric path. Optimal trajectory path planning algorithms for the omni-directional mobile robots are discussed in [3], [4], [14], [16], [17], [18]. In [14], the dynamic path planning for omni-directional robot is studied considering the robot dynamic constraints. In this paper, the main focus is on accurate trajectory following control, given a feasible trajectory command within the robot physical limitations. While optimal dynamic path planning is not within the scope of the paper, an ad hoc yet effective time-varying bandwidth command shaping filter is employed for actuator saturation and integrator windup avoidance, in the presence of an abrupt command trajectory violating the robot’s dynamic constraints.

The omni-directional robot controller design has been studied based on different robot dynamics models. In an early version of Robocat controller [6], [14], which is similar to [16], only kinematics are considered in the controller design. Each motor is controlled by an individual PID controller to follow the speed command from inverse kinematics. Without considering the coupled nonlinear dynamics explicitly in the controller design, the trial-and-error process of tuning the PID controller gains is tedious [14]. In [3], [17], [19], kinematics and dynamics models of omni-directional mobile robots have been developed, which include the motor dynamics but ignored the nonlinear coupling between the rotational and translational velocities. Thus the robot dynamics model is simplified as a linear system. In [3], [4], [17], optimal path planning and control strategies have been developed for position control without considering orientation control, and the designed controller was tested in simulations and experiment. In [19], two independent PID controllers are designed for controlling position and orientation separately based on the simplified linear model. In [6], [7], [8], [14], a nonlinear dynamic model including the nonlinear coupling terms has been developed. In [7], a resolved-acceleration control with PI and PD feedback has been developed to control the robot speed and orientation angle. It is essentially a feedback linearization control. That controller design is tested on the robot hardware. In [8], based on the same model in [7], PID, self tuning PID, and fuzzy control of omni-directional mobile robots have been studied. In [12], a variable-structure-like nonlinear controller has been developed for general wheel robot with kinematics disturbance, in which a globally uniformly ultimately bounded stability (GUUB) is achieved. In [27], feedback linearization control for wheeled mobile robot kinematics has been developed and tested on a two-wheel nonholonomic robot. In [28], a fuzzy tracking controller has been developed for a four-wheel differentially steered robot without explicit model of the robot dynamics.

In this paper first, a detailed nonlinear dynamics model of the omni-directional robot is presented, in which both the motor dynamics and robot nonlinear motion dynamics are considered. Instead of combining the robot kinematics and dynamics together as in [6], [7], [8], [14], the robot model is represented by the separated kinematics equation and the body frame dynamics equation. Such representation facilitates the robot motion analysis and controller design.

Second, based on the nonlinear robot model, a 3-degrees-of-freedom (3DOF) robot tracking controller design, using a nonlinear control method, is presented. To simplify the design, a two-loop controller architecture is employed based on the time-scale separation principle and singular perturbation theory. The outer-loop controller is a kinematics controller. It adjusts the robot position and orientation to follow the commanded trajectory. The inner-loop is a dynamics controller which follows the body rate command given by the outer-loop controller. Both outer-loop and inner-loop controllers employ a nonlinear control method based on linearization along a nominal trajectory. It is known as trajectory linearization control (TLC) [10]. Preliminary results of the proposed robot TLC controller have been summarized in [9]. It is worth noting that the presented controller can be used as a velocity and orientation controller, which is similar to the controller structure in [7]. TLC combines the nonlinear dynamic inversion and linear time-varying eigenstructure assignment in a novel way, and has been successfully applied to missile and reusable launch vehicle flight control systems [10], [11]. The nonlinear tracking and decoupling control by trajectory linearization can be viewed as an ideal gain-scheduling controller designed at every point on the trajectory. TLC can achieve exponential stability along the nominal trajectory, therefore it provides robust stability and performance along the trajectory without interpolation of controller gains. The developed robot TLC controller serves as both position controller and trajectory following control with the same set controller parameters. Compared with the nonlinear controllers in [12], [27], the proposed TLC mobile robot controller deals with both kinematic disturbances (outer-loop controller) and dynamic disturbance (inner-loop controller). Compared with [12], the TLC controller can achieve robust performance under less strict assumptions, while eliminating the chattering control signals in [12]. It should be noted that the structure of TLC is different from another nonlinear control method—feedback linearization control (FLC) [30], [31], [32]. In an FLC design, a nonlinear dynamic system is transformed to a linear system via a nonlinear coordinate transformation and a nonlinear state feedback that cancels the nonlinearity in the transformed coordinates. Then a linear time-invariant (LTI) controller is designed for the transformed linear system to satisfy the disturbance and robustness requirements for the overall system. The FLC relies on the nonlinearity cancellation in the transformed coordinate via nonlinear state feedback. In an actual control system, the cancellation of nonlinear terms will not be exact due to modeling errors, uncertainties, measurement noise and lag, and the existence of parasitic dynamics. The LTI feedback controller designed under the nominal conditions may not effectively handle the nonlinear time-varying residual dynamics.

Third, a sensor fusion scheme for robot position and orientation measurements is presented. From real-time experiments, it is observed that the accurate position and orientation measurements are essential for the controller performance. On-board sensors, such as motor shaft encoders, can be used to estimate robot location and orientation by integrating the measured robot velocity. Such estimation is fast, but also has inevitable cumulative errors introduced by the wheel slippage and the sensor noise. Calibration methods for mobile robot odometry have been developed to reduce the position estimation error [25], [26]. While these methods have enhanced the accuracy of odometry position estimation, the estimation drift cannot be eliminated without an external reference. On the other hand, global position reference sensors, such as a vision system using a roof camera senses the robot location and orientation directly without drifting. However, it is relatively slow and sometimes unreliable due to the image processing and communication errors. Thus, a sensor fusion technique is presented, which combines both the global vision system and on-board sensor estimation to provide an accurate and reliable location measurement. It is based on a nonlinear Kalman filter using trajectory linearization.

In Section 2, the omni-directional mobile robot dynamics model is presented. Based on this model, in Section 3, a dual-loop robot TLC controller is developed. In Section 4, the sensor fusion method is described. In Section 5, controller parameter tuning and the time-varying bandwidth command shaping filter are discussed. In Section 6, real-time hardware-in-the-loop (HIL) test results are presented.