Momentum-Aware Trajectory Optimisation using Full-Centroidal Dynamics and Implicit Inverse Kinematics

TL;DR

This work exploits the system's high-order nonlinearities, such as the nonholonomy of the angular momentum, in order to produce feasible, high-acceleration manoeuvres, and shows that the robot's dynamics can be exploited to surpass its hardware limitations of having a high mass and low-torque limits.

Abstract

The current state-of-the-art gradient-based optimisation frameworks are able to produce impressive dynamic manoeuvres such as linear and rotational jumps. However, these methods, which optimise over the full rigid-body dynamics of the robot, often require precise foothold locations apriori, while real-time performance is not guaranteed without elaborate regularisation and tuning of the cost function. In contrast, we investigate the advantages of a task-space optimisation framework, with special focus on acrobatic motions. Our proposed formulation exploits the system's high-order nonlinearities, such as the nonholonomy of the angular momentum, in order to produce feasible, high-acceleration manoeuvres. 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. Finally, we deploy our proposed framework on the ANYmal C platform, and demonstrate its true capabilities through real-world experiments, with the successful execution of high-acceleration motions, such as linear and rotational jumps. Extensive analysis of these shows that the robot's dynamics can be exploited to surpass its hardware limitations of having a high mass and low-torque limits.

Figures (3)

• Figure 1: ANYmal C performing a squat-jump: The proposed TO framework manages to overcome the limitations imposed by the high-mass of the robot and its low torque limits and successfully performs a jump. ANYmal's WBC runs at 400Hz and its not designed for acrobatic motions, hence it presents deficit tracking performance, which is partially mitigated by tuning its parameters exhaustively. The controller takes the desired state trajectory from the proposed TO framework and produces the required torques for the jump, while no re-planning is used to further highlight the ability of the proposed formulation to produce feasible, long-horizon trajectories.
• Figure 2: A linear squat-jump as deployed on the real ANYmal C robot. The top row shows the robot manoeuvre during five distinct phases: (a) the initial condition, (b) the squat phase, (c) in-flight phase, (d) landing period, and (e) return to initial conditions. The snapshots of the robot found in the first row are accompanied by the trajectories for the base height (row 2), foot-swing (row 3) and the measured joint torques (row 4). The input regularisation to the TO is the desired reference height as indicated in the base-height plot, while no references are required for the swing trajectories. The measured torques during the manoeuvre do not violate the torque limits of 75Nm even during touchdown. The negative foot height after touchdown is attributed to state-estimation drift, as the state estimator is not designed to handle flight phases with sudden impacts effectively.
• Figure 3: A 40 rotational jump deployed on the real robot. Only the desired yaw angle and base-height are provided to the solver, along with an approximate regularisation for the feet locations at touchdown. The top row of this figure shows five snapshots during the agile manoeuvre: (a) the initial condition, (b) squat phase, (c) flight phase, (d) landing phase and (e) return to initial conditions. The second and third rows show the base height and yaw trajectories. The fourth row shows the foot-swing tracking, while the final row shows the measured torques for the front left leg which evolve smoothly and do not violate the torque limits of 75Nm. Note the smooth evolution of the angular velocity before and during the flight-phase, indicating the good inertia tracking capabilities of the controller. The yaw velocity is brought close to zero during the flight-phase in order to land smoothly and not violate the friction-cone constraint at touchdown.The negative foot-height after touchdown is attributed to state-estimation drift, as the state estimator is not designed to handle flight phases with sudden impacts effectively.