In order to obtain high-precision 3D mapping for domestic cleaning robots and address the limitations of traditional planar calibration methods—such as overfitting and low calibration accuracy, an improved extrinsic calibration method based on three-cylinder geometric constraints is proposed. Side-scan data from three fixed congruent cylinders using the two different sensors are obtained at different positions by varying the robot’s poses. For the three elliptical contours generated by the intersection of the LDS sensor, the RANSAC algorithm is employed to extract the center points of these contours and two randomly selected points on each contour. For the 3D point cloud of the cylinder surfaces captured via the ToF depth sensor, the central axes of the three cylinders are fitted using the RANSAC algorithm. Spatial geometric constraints are established using the three center points from the elliptical contours and the distances from the two randomly selected points on each contour to their corresponding cylinder axes, forming a system of nonlinear optimization equations for extrinsic parameter estimation. To enhance solving stability, an improved optimization strategy integrating the Powell algorithm and the quasi-Newton BFGS algorithm is proposed, effectively addressing the dependency on initial parameter values. Simulation experiments are conducted to analyze the impact of initial values and Gaussian noise. The proposed method achieves an average rotation error of 0.37° and an average translation error of 3.2 mm, demonstrating rapid convergence even with significant initial offsets. Finally, real experiments and comparative 3D mapping tests are performed to verify the effectiveness of the algorithm. The results show that the proposed method is insensitive to initial parameter values, offers operational simplicity and high calibration accuracy, and possesses significant value for practical engineering applications.