An approach to the dynamic modeling and sliding mode control of the constrained robot is proposed in this article. On the basis of the Udwadia-Kalaba approach, the explicit equation of the constrained robot system is obtained first. This equation is applicable to systems with either holonomic or non-holonomic constraints, as well as with either ideal or non-ideal constraint forces. Second, fully considering the uncertainty of the non-ideal force, that is, the dynamic friction in the constrained robot system, the sliding mode control algorithm is put forward to trajectory tracking of the endeffector on a vertical constrained surface to obtain actual values of the unknown constraint force. Moreover, model order reduction method is innovatively used in the Udwadia-Kalaba approach and sliding mode controller to reduce variables and simplify the complexity of the calculation. Based on the demonstration of this novel method, a detailed robot system example is finally presented.

Abstract. Knapsack problem, a typical problem of combinatorial optimization in operational research, has broad applied foregrounds. This paper applies particle swarm optimization to solve discrete 0/1 knapsack problem. However, traditional particle swarm optimization has nonnegligible disadvantages: all the parameters in the formula affect the abilities of local searching and global searching greatly, which is liable to converge too early and fall into the situation of local optimum. This paper modifies traditional particle swarm optimization, and makes the position of particle which achieves global optimization reinitializated. Through analyzing the final result, the paper has proven that the improved algorithm could improve searching ability of particle swarm, avoid converging too early and solve 0/1 knapsack problem more effectively.

A reduced-order approach to the adaptive fuzzy sliding mode control of the constrained manipulator is proposed. Based on the Udwadia–Kalaba motion constraint equation, the dynamic equation of the constrained manipulator with both ideal and non-ideal constraints is obtained. Considering the uncertainty of the terminal non-ideal constrained force and the chattering phenomenon of sliding mode control, the adaptive fuzzy and the sliding mode control method are combined to control the constrained manipulator. Because the system is constrained, the model order reduction method is innovatively used in the control algorithm. The stability of the system is proved by Lyapunov theorem. For demonstrating the effectiveness of the control algorithm, the 2-degree-of-freedom manipulator is taken as the research object. Finally, the high-precision control of the manipulator is achieved and the chattering phenomenon caused by the sliding mode control is weakened.

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