Aiming to deal with underwater localization for small-size robots in GPS-denied and structured environment, this paper proposed a novel multi-sensor fusion-based self-localization system using low-cost sensors. Based on multi-sensor information fusion, an Extended Kalman Filter (EKF) is utilized to synthesize the multi-source information from an Inertial Measurement Unit (IMU), optical flow, pressure sensor and ArUco markers, which enables the robot obtain a highly precise positioning. This method also can reduce the location drift over time owing to the loss of markers in pure markers-based localization. Specially, a velocity correction model is proposed using the angle information obtained by IMU, which can compensate optical flow-based velocity estimation errors caused by robot posture changes. Finally, to validate the performance of the proposed self-localization system, simulations are conducted using Gazebo simulator on the robot operating system (ROS). Moreover, a series of experiments in an indoor swimming pool are presented. Results of the proposed method and dead reckoning are compared in simulation and experiment to demonstrate the robustness and feasibility of the proposed localization system.

We describe the novel, multiply gaited, vectored water-jet, hybrid locomotion-capable, amphibious spherical robot III (termed ASR-III) featuring a wheel-legged, water-jet composite driving system incorporating a lifting and supporting wheel mechanism (LSWM) and mechanical legs with a water-jet thruster. The LSWM allows the ASR-III to support the body and slide flexibly on smooth (flat) terrain. The composite driving system facilitates two on-land locomotion modes (sliding and walking) and underwater locomotion mode with vectored thrusters, improving adaptability to the amphibious environment. Sliding locomotion improves the stability and maneuverability of ASR-III on smooth flat terrain, whereas walking locomotion allows ASR-III to conquer rough terrain. We used both forward and reverse kinematic models to evaluate the walking and sliding gait efficiency. The robot can also realize underwater locomotion with four vectored water-jet thrusters, and is capable of forward motion, heading angle control and depth control. We evaluated LSWM efficiency and the sliding velocities associated with varying extensions of the LSWM. To explore gait stability and mobility, we performed on-land experiments on smooth flat terrain to define the optimal stride length and frequency. We also evaluated the efficacy of waypoint tracking when the sliding gait was employed, using a closed-loop proportional-integral-derivative (PID) control mechanism. Moreover, experiments of forward locomotion, heading angle control and depth control were conducted to verify the underwater performance of ASR-III. Comparison of the previous robot and ASR-III demonstrated the ASR-III had better amphibious motion performance.

Thrusters are the bottom actuators of the amphibious spherical robot, and play an important role in the motion control of these robots. To realize accurate motion control, a thrust model for a new water-jet thruster based on hydrodynamic analyses is proposed in this paper. First, the hydrodynamic characteristics of the new thruster were numerically analyzed using computational fluid dynamics (CFD) commercial software CFX. The moving reference frame (MRF) technique was utilized to simulate propeller rotation. In particular, the hydrodynamics of the thruster were studied not only in the axial flow but also in oblique flow. Then, the basic framework of the thrust model was built according to hydromechanics theory. Parameters in the basic framework were identified through the results of the hydrodynamic simulation. Finally, a series of relevant experiments were conducted to verify the accuracy of the thrust model. These proved that the thrust model-based simulation results agreed well with the experimental results. The maximum error between the experimental results and simulation results was only 7%, which indicates that the thrust model is precise enough to be utilized in the motion control of amphibious spherical robots.

To improve the autonomy of the biomimetic sphere robot (BSR), an underwater trajectory tracking problem was studied. Considering the thrusters saturation of the BSR, an improved model predictive control (MPC) algorithm that features processing multiple constraints was designed. With the proposed algorithm, the kinematic and dynamic models of the BSR are combined in order to establish the predictive model, and a new state-space model is designed that is based on an increment of the control input. Furthermore, to avoid the infeasibility of the cost function in the MPC controller design, a new term with a slack variable is added to the objective function, which enables the constraints to be imposed as soft constraints. The simulation results illustrate that the BSR was able to track the desired trajectory accurately and stably while using the improved MPC algorithm. Furthermore, a comparison with the traditional MPC shows that the designed MPC-based increment of the control input is small. In addition, a comparative simulation using the backstepping method verifies the effectiveness of the proposed method. Unlike previous studies that only focused on the simulation validations, in this study a series of experiments were carried out that further demonstrate the effectiveness of the improved MPC for underwater trajectory tracking of the BSR. The experimental results illustrate that the improved MPC is able to drive the BSR to quickly track the reference trajectory. When compared with a traditional MPC and the backstepping method used in the experiment, the proposed MPC-based trajectory is closer to the reference trajectory.

Due to the characteristics of good concealment ability and strong mobility, multiple, small spherical underwater robot formations play an important role in near coast defense missions, such as cruising, reconnaissance, surveillance, and sensitive target capturing. Referring to the formation problem for underwater small spherical robots with limited energy, perception, and computation abilities, a trajectory tracking-based formation strategy that transforms the complex formation tracking problem into a simple trajectory tracking problem of a single robot is provided. Two layers are designed in the formation tracking strategy. The upper layer is a virtual structure-based formation algorithm. The bottom layer is a tracking controller based on model predictive control (MPC). The formation algorithm is in charge of calculating reference trajectory for each robot in the formation according to the global formation path. The MPC-based dynamic controller for each robot is designed to track the self reference trajectory. Compared with the model predictive control method used for the traditional trajectory tracking problem of a single robot, this paper additionally considers the formation constraints and the internal collision avoidance. In addition, the extended state observer (ESO) is utilized to estimate the lumped disturbance composed of environment disturbance and the inaccurate dynamic model of a small spherical robot. Not only are the numerical simulations based on MATLAB v.2015a, but physical simulations based on self-building multi-spherical robot formation platform are also carried out. Furthermore, through using two small spherical robots, a formation tracing experiment is conducted. All of the results prove that the proposed formation method is feasible and practical for small spherical robots.

In this paper, a double closed-loop backstepping controller is designed for 3D trajectory tracking of a turtle-inspired amphibious spherical robot suffering from problems that include model uncertainties, environmental disturbances, and unmeasured velocity. The proposed controller scheme tackles three primary challenges: the differentiation explosion of the traditional backstepping method, unmeasured velocity, and the consideration of lumped disturbances. Beginning with an outer-loop backstepping controller, a virtual feedback variable is constructed to simplify the design of the backstepping controller. Meanwhile, to avoid the problem of differentiation explosion, tracking differentiators (TDs) are utilized to estimate the differentiation of the desired velocity in an inner-loop backstepping controller. Moreover, there are some uncertainty disturbances in the task of tracking the trajectory of a turtle-inspired amphibious spherical robot (TASR), such as the parameters of the hydrodynamic model and environmental disturbances. A linear extended state observer (LESO) is designed to estimate and compensate for the lumped disturbances. Furthermore, as the velocity states of the TASR are unmeasured, the LESO is also utilized to estimate the velocity states in surge, yaw, and heave degrees. Therefore, the TASR only needs to supply its position and orientation information for the trajectory tracking task. Note that this paper details both the design process of the proposed controller and a rigorous theoretical analysis. In addition, numerical simulations are conducted, and the results demonstrate the feasibility and superiority of the proposed method.