In this article, a novel mechanism for planar one-legged hopping robots is proposed. The robot consists of a flat foot which is pinned to the leg and a reciprocating mass which is connected to the leg via a prismatic joint. The proposed mechanism performs the hopping by transferring linear momentum between the reciprocating mass and its main body. The nonlinear equations of the motion of the robot are derived using the Euler–Lagrange equations. To accomplish a stable jump, appropriate trajectories have been planned. To guarantee a stable response for this nonlinear system, a sliding-mode controller is implemented. The performance of the hopping robot is investigated through numerical simulations. The results confirm the stability of the hopping robot through the jump cycle on a flat surface and in climbing up and down ramp and stairs.

This paper presents a novel robust hybrid fractional order proportional derivative sliding mode controller (HFOPDSMC) for 2-degree of freedom (2-DOF) robot manipulator based on extended grey wolf optimizer (EGWO). Sliding mode controller (SMC) is remarkably robust against the uncertainties and external disturbances and shows the valuable properties of accuracy. In this paper, a new fractional order sliding surface (FOSS) is defined. Integrating the fractional order proportional derivative controller (FOPDC) and a new sliding mode controller (FOSMC), a novel robust controller based on HFOPDSMC is proposed. The bounded model uncertainties are considered in the dynamics of the robot, and then the robustness of the controller is verified. The Lyapunov theory is utilized in order to show the stability of the proposed controller. In this paper, the EGWO is developed by adding the emphasis coefficients to the typical grey wolf optimizer (GWO). The GWO and EGWO, then, are applied to optimize the proposed control parameters which result in the optimized GWO-HFOPDSMC and EGWO-HFOPDSMC, respectively. The effectivenesses of the optimized controllers (GWO-HFOPDSMC and EGWO-HFOPDSMC) are completely verified by comparing the simulation results of the optimized controllers with the typical FOSMC and HFOPDSMC.

Designing the boundary layer thickness and switching gain in the nonlinear part of sliding mode controller (SMC) is one of the main subjects in SMC design that needs human experience, knowledge on the amplitude of disturbances, and information about the bounds of system uncertainties. In this paper, to reduce the trial-and-error effort by the designer(s) two different fitness functions in the horizontal and vertical planes are presented and a heuristic method is used for their optimization. The optimal switching gain in the proposed approach properly compensates the unmodeled dynamics, model uncertainty, and external disturbances. Chattering phenomenon in control signals and noise measurement effect are reduced by the optimal selection of boundary layer thickness. This proposed method is applied to an autonomous underwater vehicle (AUV) and evaluated through the real-time and cost-effective manner. The execution code is implemented on a single-board computer (SBC) through the xPC Target and is evaluated by the processor-in-the-loop (PIL) test. The results of the PIL test in the two different test cases indicate that the chattering phenomenon and amplitude of control signal applied to the actuators are reduced in comparison with the three conventional approaches in the AUV motion control.

Although robots have some kinematic and dynamic constraints such as the limits of the position, velocity, acceleration, jerk, and torque, they should move as fast as possible to increase the productivity. Researches on the minimum-time trajectory planning and control based on the dynamic constraints assume the availability of full dynamics of robots. However, the dynamic equation of robot may not often be exactly known. In this case, the kinematic approach for the minimum-time trajectory planning is more meaningful. We also have to construct a controller to track precisely the minimum-time trajectory. But, finding a proper controller is also difficult if we do not know the explicit dynamic equations of a robot.

This paper describes an optimization of trajectory planning based on a kinematic approach using the evolution strategy (ES), as well as an optimization of a sliding mode tracking controller using ES for a robot without dynamic equations.