<p>This paper presents the design of a circular-orbit redundant heterogeneous robotic system intended to replace manual labor in the task of pushing materials within high-temperature coal furnaces. A mathematical constraint model for the robotic system was constructed, and the structural parameters of the heterogeneous components were determined. The feasibility of these structural parameters was validated through simulation experiments. For the inverse kinematics problem of redundant heterogeneous robotic systems with offset joints, this study proposes a novel inverse kinematics algorithm based on screw theory and three-dimensional offset matrices, effectively addressing the geometric complexities and nonlinear challenges introduced by the offset joint configuration. To address the issues of poor path smoothness and significant velocity discontinuities in traditional NSGA-II algorithms during trajectory planning in complex scenarios, this study proposes a dynamic window and dualfitness enhanced nondominated sorting genetic algorithm II (DWDF-NSGA-II) under complex strongly coupled constraints. Experimental results demonstrate that the DWDF-NSGA-II algorithm generates end-effector trajectories with superior path length and motion smoothness compared to those planned by conventional algorithms, effectively addressing trajectory planning challenges for robotic end-effectors under multi-constraint conditions.</p>