  Complex robotic systems require whole-body controllers to deal with contact
interactions, handle closed kinematic chains, and track task-space control
objectives. However, for many applications, safety-critical controllers are
important to steer away from undesired robot configurations to prevent unsafe
behaviors. A prime example is legged robotics, where we can have tasks such as
balance control, regulation of torso orientation, and, most importantly,
walking. As the coordination of multi-body systems is non-trivial, following a
combination of those tasks might lead to configurations that are deemed
dangerous, such as stepping on its support foot during walking, leaning the
torso excessively, or producing excessive centroidal momentum, resulting in
non-human-like walking. To address these challenges, we propose a formulation
of an inverse dynamics control enhanced with exponential control barrier
functions for robotic systems with numerous degrees of freedom. Our approach
utilizes a quadratic program that respects closed kinematic chains, minimizes
the control objectives, and imposes desired constraints on the Zero Moment
Point, friction cone, and torque. More importantly, it also ensures the forward
invariance of a general user-defined high Relative-Degree safety set. We
demonstrate the effectiveness of our method by applying it to the 3D biped
robot Digit, both in simulation and with hardware experiments.
