Trajectory tracking control of spatial underactuated vehicles

Abstract

A common approach to control of underactuated vehicles is a prelude to cooperative control of heterogeneous networks. This article presents a novel nonlinear trajectory tracking control framework for general three-dimensional models of underactuated vehicles with twelve states and four control inputs, including underwater, air, and space vehicles. Given a desired reference trajectory for four of the six degrees of freedom, feasible state trajectories are generated using the second-order nonholonomic constraints in the vehicle equations of motion. A novel transformation is then introduced to formulate the error dynamics in a simplified form. The error dynamics is stabilized using a traditional nonlinear control approach. The control law is shown to uniformly asymptotically stabilize all six pose states assuming bounded unknown uncertainties and disturbances. Adaptation of the method to underwater vehicles is presented along with simulation under highly nonlinear conditions. The approach is also applied to quadrotors and both simulation and experimental results are presented. K E Y W O R D Sbackstepping control, trajectory tracking control, underactuated vehicles INTRODUCTIONAutonomous vehicles have become more practical and thus more prevalent as a consequence of sensors, computers, and power electronics becoming better, cheaper, and smaller. However, controlling the motion of such vehicles is complex, as they tend to be underactuated, that is, fewer actuators than degrees of freedom. These include cars, surface vessels, underwater vessels, and air vehicles. In one of our previous works 1 we considered developing a control algorithm that can be applied to any planar underactuated vehicle. We then extended that work to Spatial vehicle models but with only one degree of underactuation. 2 In this work, we attempt to develop a control algorithm applicable to a variety of spatial underactuated vehicles with two degrees of underactuation including underwater vessels and air vehicles.Considering underwater vehicles, a submarine's propeller produces a surge force along the axis of motion; this is the translational actuator. There are also rotational actuators. A rudder induces yaw motion and diving planes induce pitching motion. 3 Roll motion, however, is a bit more complicated. Many manned submarines are designed to be passively self-righting and therefore do not have active roll control, with some exceptions where roll motion is desired, such as the DeepFlight Super Falcon. 4 There are several works that ignore the roll motion or at least its coupling with the other degrees of freedom and use five degree-of-freedom (DOF) models. [5][6][7] These methods concentrate on uncertainty and disturbance rejection as well as other important topics such as actuation limits and velocity estimation. 8

Range observer‐based formation control for heterogeneous spatial underactuated vehicle networks

“…Without any loss of generality, we assume that the control thrust is in the direction of one of the three body‐fixed axes, that is, $$$ {F}_{\mathbf{i}}={\left[{F}_{x\mathbf{i}},0,0\right]}^{\top } $$$, $$$ {F}_{\mathbf{i}}={\left[0,{F}_{y\mathbf{i}},0\right]}^{\top } $$$, or $$$ {F}_{\mathbf{i}}={\left[0,0,{F}_{z\mathbf{i}}\right]}^{\top } $$$. It should be noted that the full nonlinear vehicle model ()–() can represent a wide class of spatial underactuated vehicles including AUVs ($$$ {F}_{\mathbf{i}}={\left[{F}_{x\mathbf{i}},0,0\right]}^{\top } $$$) and quadrotors ($$$ {F}_{\mathbf{i}}={\left[0,0,{F}_{z\mathbf{i}}\right]}^{\top } $$$) 15 …”

“…Unlike fully‐actuated systems, underactuated mechanical systems cannot be commanded to track arbitrary trajectories. To be more precise, for the 6‐DOF spatial vehicle model () and () with two degrees of underactuation, the desired trajectories can only be independently specified for four configuration variables 15 . Considering the formation objective (), in addition to controlling the three position variables, one attitude variable also can be independently controlled.…”

“…Note that the matrix T(𝜂) becomes singular when 𝜃 = ±𝜋∕2, and thus, we restrict the use of Euler angles to |𝜙 i | < 𝜋∕2 and |𝜃 i | < 𝜋∕2 to avoid aggressive maneuvers and singularity. 15 We consider the spatial vehicle model with two degrees of underactuation. More precisely, we assume that each vehicle has only one control thrust (force) and three control torques.…”

“…In Reference 13, a trajectory tracking control framework was proposed for generic planar vehicles, which is applicable to wheeled mobile robots, surface vessels, and planar vertical take‐off and landing (PVTOL) aircraft. Using similar ideas, the trajectory tracking control problem was solved for generic spatial vehicles with one degree of underactuation in Reference 14, and spatial vehicles with two degrees of underactuation in Reference 15.…”

Adaptive Backstepping Sliding Mode Tracking Control For Autonomous Underwater Vehicles With Input Quantization

“…[1][2][3] With the rapid development of ocean engineering, increasing attention is paid to the tracking control of AUVs. [4] However, in the complex and unpredictable ocean environment, precise tracking control of AUVs is very difficult due to the highly nonlinear dynamics, time varying external disturbance and uncertainties in hydrodynamic coefficients. [5] The uncertainties and environmental disturbances like waves and ocean currents can degrade system performance, damage equipment, and even lead to system instability.…”