In this study, a new cable-driven rehabilitation robot is designed, the overall design of the robot is given, and the kinematic equation of the lower limbs in the supine state of the human body is addressed. Considering that cable winders move along the rail brackets, the closed vector method is applied to establish the kinematic model of the robot, and the relationship between the human joint angle and the cable length change was deduced. Considering joint compliance, a fifth-order polynomial trajectory planning method based on an S-shaped curve is proposed by introducing an S-shaped velocity curve, and the changes in cable length displacement, velocity, and acceleration are simulated and analyzed. Three planning methods are compared based on two indices, and experimental verification is carried out on the rehabilitation experiment platform. The simulation and experimental results show that the trajectory planning method presents low energy consumption and strong flexibility, and can achieve better rehabilitation effect, which builds a good basis for the subsequent study of dynamics and control strategy.

The stochastic resource allocation (SRA) problem, commonly seen in the decision-making of complex systems, is a typical combinatorial optimization challenge that seeks optimality, quickness, as well as generality. Among various SRA algorithms, constructive heuristics (CH) such as greedy algorithms construct feasible solutions by prioritizing optional resource-task allocation pairs based on a predefined evaluation criterion. They are very suitable for real-time decision-making due to their simplicity and low computational complexity. However, relying on a single fixed criterion can impair optimality and generality. To achieve a generalized expression for the criterion, this paper establishes a fuzzy evaluation system that determines the component priorities by leveraging SRA problem features, enabling diversified and flexible solution construction. Furthermore, for the sake of generality, this paper proposes a fuzzy-evaluation-based constructive heuristics generation framework (FCHG), which generates an ensemble of complementary CHs through automatic training. FCHG adopts an adversarial coevolution mechanism, using the SRA instance generator and evolutionary algorithms to realize competition-based coevolution between the SRA instances and CHs. For SRA problem-solving, the CH ensemble obtained by FCHG can construct multiple SRA solutions efficiently, and the best one will serve as the final solution. Comparative experiments against state-of-the-art algorithms, covering instances with varying scales and structural characteristics, demonstrate the comprehensive superiority of the CH ensemble in solving the SRA problem in terms of optimality, quickness, generality, and numerical stability.