Actuator Transparency and the Energetic Cost of Proprioception

In the field of haptics, conditions for mechanical “transparency”[1] entail such qualities as “solid virtual objects must feel stiff” and “free space must feel free”[2], suggesting that a suitable actuator is able both to do work and readily have work done on it. In this context, seeking actuator transparency has come to mean a preference for minimal dynamics [3] or no impedance [4]. While such general notions seem satisfactory for a haptic interface, actuators with good mechanical transparency are now being used in high-performance robots [5, 6] where once again they must be able to do work, but are now also expected to perceive their environment by processing signals related to contact forces in the leg or manipulator when an explicit force sensor is not present. As robotics researchers develop models [7] suitable for programming behaviors that require systematic making and breaking of contact within the environments on which they perform work, actuators must be capable of: (a) generating the high forces at speed needed to accelerate the body during locomotion [5]; (b) robustness to high forces and impacts during locomotion [8]; (c) perceiving high force events quickly, such as touchdown in stance [9]; (d) perceiving contact quickly without exerting significant force on the object, such as in gentle manipulation [10]; and (e) reacting quickly during time-sensitive behaviors [11].

This work aims to describe a quantitative assay of transparency that might, for example, predict the advantage in proprioceptive tasks of an electromagnetic directdrive (DD) motor (i.e., one without gearbox), relative to actuation schemes consisting of both a motor and a geared reduction. Specifically, we explore the prospects for characterizing transparency as revealed by comparing the energetic cost of “feeling” the environment. Our sample proprioceptive task is instantiated by a simple torque estimator in Sec. 2. This scheme is then instrumented in simple contact detection experiments paired with a model to empirically explore the relationships between collision energy and detection time delay in Sec. 3. The actuators are then tested with a feel-cage task to illustrate the advantage of good transparency in Sec. 4.

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