Differential flatness-based distributed control of underactuated robot swarms

This paper proposes a distributed control method based on the differential flatness(DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the control objective. The DF mapping refers to the fact that the system state and input of each robot can be derived algebraically from the flat outputs of the leaders and the cooperative errors and their finite order derivatives. Based on the proposed swarm DF mapping, a distributed controller is designed. The distributed implementation of swarm DF mapping is achieved through observer design. The effectiveness of the proposed method is validated through a numerical simulation of quadrotor swarm synchronization.

Trajectory Tracking Control for Under-Actuated Hovercraft Using Differential Flatness and Reinforcement Learning-Based Active Disturbance Rejection Control

This paper proposes a scheme of trajectory tracking control for the hovercraft.Since the model of the hovercraft is under-actuated,nonlinear,and strongly coupled,it is a great challenge for the controller design.To solve this problem,the control scheme is divided into two parts.Firstly,we employ differential flatness method to find a set of flat outputs and consider part of the nonlinear terms as uncertainties.Consequently,we convert the under-actuated system into a full-actuated one.Secondly,a reinforcement learning-based active disturbance rejection controller(RL-ADRC)is designed.In this method,an extended state observer(ESO)is designed to estimate the uncertainties of the system,and an actorcritic-based reinforcement learning(RL)algorithm is used to approximate the optimal control strategy.Based on the output of the ESO,the RL-ADRC compensates for the total uncertainties in real-time,and simultaneously,generates the optimal control strategy by RL algorithm.Simulation results show that,compared with the traditional ADRC method,RL-ADRC does not need to manually tune the controller parameters,and the control strategy is more robust.

Optimal Motion Planning for Differentially Flat Underactuated Mechanical Systems

Underactuated mechanical system has less independent inputs than the degrees of freedom（DOF） of the mechanism. The energy efficiency of this class of mechanical systems is an essential problem in practice. On the basis of the sufficient and necessary condition that concludes a single input nonlinear system is differentially flat, it is shown that the flat output of the single input underactuated mechanical system can be obtained by finding a smooth output function such that the relative degree of the system equals to the dimension of the state space. If the flat output of the underactuated system can be solved explicitly, and by constructing a smooth curve with satisfying given boundary conditions in fiat output space, an energy efficiency optimization method is proposed for the motion planning of the differentially flat underactuated mechanical systems. The inertia wheel pendulum is used to verify the proposed optimization method, and some numerical simulations show that the presented optimal motion planning method can efficaciously reduce the energy cost for given control tasks.

Flatness-Based Control in Successive Loops for Unmanned Aerial Vehicles and Micro-Satellites

The control problem for the multivariable and nonlinear dynamics of unmanned aerial vehicles and micro-satellites is solved with the use of a flatness-based control approach which is implemented in successive loops.The state-space model of(i)unmanned aerial vehicles and(ii)micro-satellites is separated into two subsystems,which are connected between them in cascading loops.Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input–output linearized flat systems.The state variables of the second subsystem become virtual control inputs for the first subsystem.In turn,exogenous control inputs are applied to the first subsystem.The whole control method is implemented in two successive loops and its global stability properties are also proven through Lyapunov stability analysis.The validity of the control method is confirmed in two case studies:(a)control and trajectories tracking for the autonomous octocopter,(ii)control of the attitude dynamics of micro-satellites.