The purpose of this paper is two-fold. First, the smoothness of the distributed consensus control (DCC) protocols of multi-agent systems (MAS) with inherent nonlinear dynamics is investigated. Different from the traditional consensus protocols where variable structure control is considered for robust control, a continuous DCC is presented to achieve consensus tracking without control chattering. Using certain types of exponential functions, it is shown that different smooth DCC schemes can be constructed to achieve asymptotic consensus tracking with smooth control input for MAS with connected directed/undirected and fixed/switched communication topologies. Second, the formation control problem of nonholonomic wheeled mobile robots (WMR) is solved via the continuous DCC. By converting the formation problem into consensus problem using the agents’ kinematics, the formation speed-control problem in planar motion is formulated and solved. The translational and rotational speeds inputs to the WMR are computed using continuous distributed consensus protocols to reduce chattering in the control inputs of mobile robots. The distinctive feature of the proposed consensus and formation algorithms is the high tracking precision with smooth control input to agents’ dynamics. In simulation studies, different numerical examples are illustrated to demonstrate the performance and effectiveness of the proposed DCC.

This paper presents a high-order sliding mode approach to design variable structure controllers for nonlinear multivariable cross-coupling systems whereby a change in either control input affects the control loops of all the subsystems dynamics. A hybrid-sliding mode control (hybrid-SMC) scheme is constructed combining a new equivalent control algorithm with a high-order discontinuous control algorithm to benefit from the advantages of both control strategies. The hybrid-SMC scheme uses weighting coefficients to weight and combine controllers. The equivalent control algorithm uses a relative degree concept through dynamic constraints imposed on the sliding variables to overcome the limitations of the conventional approaches and to provide an optimum tracking performance. A scale-laboratory helicopter model is used to sum up the main features and demonstrate the effectiveness of the developed control scheme. The proposed hybrid-SMC strategy is compared to existing sliding mode-based control approaches in terms of tracking performance, stability and control efforts. The obtained results demonstrate the validity and efficiency of the proposed hybrid-SMC scheme.