Towards Agility: A Momentum Aware Trajectory Optimisation Framework using Full-Centroidal Dynamics & Implicit Inverse Kinematics

Online planning and execution of acrobatic maneuvers pose significant challenges in legged locomotion. Their underlying combinatorial nature, along with the current hardware's limitations constitute the main obstacles in unlocking the true potential of legged-robots. This letter tries to expose the intricacies of these optimal control problems in a tangible way, directly applicable to the creation of more efficient online trajectory optimisation frameworks. By analysing the fundamental principles that shape the behaviour of the system, the dynamics themselves can be exploited to surpass its hardware limitations. More specifically, a trajectory optimisation formulation is proposed that exploits the system's high-order nonlinearities, such as the nonholonomy of the angular momentum, and phase-space symmetries in order to produce feasible high-acceleration maneuvers. By leveraging the full-centroidal dynamics of the quadruped ANYmal C and directly optimising its footholds and contact forces, the framework is capable of producing efficient motion plans with low computational overhead. The feasibility of the produced trajectories is ensured by taking into account the configuration-dependent inertial properties of the robot during the planning process, while its robustness is increased by supplying the full analytic derivatives & hessians to the solver. Finally, a significant portion of the discussion is centred around the deployment of the proposed framework on the ANYmal C platform, while its true capabilities are demonstrated through real-world experiments, with the successful execution of high-acceleration motion scenarios like the squat-jump.