Stable Transition of Quadruped Rhythmic Motion Using the Tracking Differentiator

Since the quadruped robot possesses predominant environmental adaptability,it is expected to be employed in nature environments. In some situations,such as ice surface and tight space,the quadruped robot is required to lower the height of center of gravity( COG) to enhance the stability and maneuverability. To properly handle these situations,a quadruped controller based on the central pattern generator( CPG) model,the discrete tracking differentiator( TD) and proportional-derivative( PD) sub-controllers is presented. The CPG is used to generate basic rhythmic motion for the quadruped robot. The discrete TD is not only creatively employed to implement the transition between two different rhythmic medium values of the CPG which results in the adjustment of the height of COG of the quadruped robot,but also modified to control the transition duration which enables the quadruped robot to achieve the stable transition. Additionally,two specific PD sub-controllers are constructed to adjust the oscillation amplitude of the CPG,so as to avoid the severe deviation in the transverse direction during transition locomotion. Finally,the controller is validated on a quadruped model. A tunnel with variable height is built for the quadruped model to travel through. The simulation demonstrates the severe deviation without the PD sub-controllers,and the reduced deviation with the PD sub-controllers.

A Hybrid Learning Method for the Data-Driven Design of Linguistic Dynamic Systems

In lots of data based prediction or modeling applications,uncertainties and/or noises in the observed data cannot be avoided.In such cases,it is more preferable and reasonable to provide linguistic(fuzzy)predicted results described by fuzzy memberships or fuzzy sets instead of the crisp estimates depicted by numbers.Linguistic dynamic system(LDS)provides a powerful tool for yielding linguistic(fuzzy)results.However,it is still difficult to construct LDS models from observed data.To solve this issue,this paper first presents a simplified LDS whose inputoutput mapping can be determined by closed-form formulas.Then,a hybrid learning method is proposed to construct the data-driven LDS model.The proposed hybrid learning method firstly generates fuzzy rules by the subtractive clustering method,then carries out further optimization of centers of the consequent triangular fuzzy sets in the fuzzy rules,and finally adopts multiobjective optimization algorithm to determine the left and right end-points of the consequent triangular fuzzy sets.The proposed approach is successfully applied to three real-world prediction applications which are:prediction of energy consumption of a building,forecasting of the traffic flow,and prediction of the wind speed.Simulation results show that the uncertainties in the data can be effectively captured by the linguistic(fuzzy)estimates.It can also be extended to some other prediction or modeling problems,in which observed data have high levels of uncertainties.

Time-varying formation finite-time tracking control for multi-UAV systems under jointly connected topologies

Purpose–The purpose of this paper is to investigate the time-varying finite-time formation tracking control problem for multiple unmanned aerial vehicle systems under switching topologies,where the states of the unmanned aerial vehicles need to form desired time-varying formations while tracking the trajectory of the virtual leader in finite time under jointly connected topologies.Design/methodology/approach–A consensus-based formation control protocol is constructed to achieve the desired formation.In this paper,the time-varying formation is specified by a piecewise continuously differentiable vector,while the finite-time convergence is guaranteed by utilizing a non-linear function.Based on the graph theory,the finite-time stability of the close-loop system with the proposed control protocol under jointly connected topologies is proven by applying LaSalle’s invariance principle and the theory of homogeneity with dilation.Findings–The effectiveness of the proposed protocol is verified by numerical simulations.Consequently,the proposed protocol can successfully achieve the predefined time-varying formation in finite time under jointly connected topologies while tracking the trajectory generated by the leader.Originality/value–This paper proposes a solution to simultaneously solve the control problems of time-varying formation tracking,finite-time convergence,and switching topologies.