Smooth Optimization of Foot Trajectory Based on High-Order Polynomials and Quadratic Programming

A quadruped robot needs to have stable motion ability to overcome road obstacles and walk quickly. The impact generated by the lifting and landing of the foot end has a negative impact on the robot's motion. In order to reduce the periodic impact of the initial contact between the foot end and the ground, it is particularly important to plan a smooth and impact free foot trajectory. When using complex functions to fit motion boundary conditions, segmentation is required in the vertical direction, and the acceleration function will distort at the segmentation points. Traditional polynomial trajectory planning has inconsistent interpolation functions of different orders, and there is no quantitative standard to evaluate the interpolation effect. In response to the problem of numerical distortion in segmented points, this paper proposes the introduction of an optimization objective function as an evaluation criterion, while also increasing the dimension of trajectory constraints. The quadratic programming problem is solved through the KKT principle. The experimental results of three methods show that the trajectory planning method proposed in this paper has the advantages of strong trajectory crossing ability and low output driving torque.