A Novel Contact‐Implicit Trajectory Optimization Framework for Quadruped Locomotion without Fixed Contact Sequences

Legged robots have advanced in environmental interaction through contact, but most works rely on fixed contact sequences. To enable automatic generation of contact sequences for more complex locomotion tasks, a novel contact‐implicit trajectory optimization (TO) framework based on an Accelerated Computation Augmented Lagrangian iterative Linear Quadratic Regulator (ACAL‐iLQR) method for legged locomotion is proposed. Unlike traditional contact models, it employs a compliant contact model that ensures accurate numerical differentiation and physical realism. Building upon the full‐order dynamics of legged robots and the compliant contact model, the contact‐implicit TO problem is formulated. To prevent infeasible or nonsmooth trajectories, joint torque limits are incorporated as inequality constraints handled by the Augmented Lagrangian (AL) method within iLQR. To accelerate the optimization process, the Accelerated Computation (AC) method is introduced, which accelerates optimization by identifying key timesteps and performing linear interpolation between them, thereby decreasing the computational burden. The framework's capability to automatically generate contact sequences without predefined gait patterns is validated through three simulation tasks on the Unitree A1 robot. Comprehensive comparisons demonstrate that the proposed method achieves smoother performance than standard iLQR, reducing the total variation of torques by 42.04% while reducing optimization time by 22.83% compared to AL‐iLQR.