Comparative design, modeling, and control analysis of robotic transmissions

Abstract

Transmission dynamics are shown to dominate the stability and performance of impedance- and torque controlled rotary electro-mechanical systems. The experimental analysis focuses on planetary, cycloidal, harmonic and cable reducers, but excludes direct-drive, pneumatic, hydraulic and friction drives. Neither sensors nor actuators with better resolution nor increased dynamic range can circumvent reduced stability and performance limitations unless certain hardware criteria can be met Simple transmission models are proposed to model such effects as (1) transmission stiffness, (2) soft-zones and wind-up, (3) backlash and lost motion, and (4) stiction, friction and viscous losses. These models are experimentally verified using six different transmission types most commonly used in robot designs. Simple lumped-parameter linear/nonlinear models are shown to predict stability margins and bandwidths at these margins fairly closely. Simple nonlinear lumped- and fixed-parameter models were unable to properly predict time responses when the torque signals were of low-frequency and amplitude, underscoring the complexity in modeling the transmission-internal stick-slip phenomena. The clear distinction between speed reducers and torque multipliers is theoretically and experimentally explored. The issue of actuator and sensor colocation is shown to be extremely important in predicting the reduced bandwidth and stability of torque-controlled actuator-transmission-load systems. Stiffening transmission behaviors are shown to be of a conditionally stabilizing nature, while also reducing the dynamic range of impedance- and torque-servoed systems. System damping, whether active or passive, as well as low-pass filtering motor-controller signals, are shown to dramatically increase stability without having any effect on increasing system bandwidth. Transmission soft-zones are proven to reduce the stability margins of colocated impedance controlled electro-mechanical systems. None of the standard controller structures explored here were able to noticeably increase the system bandwidth of the open-loop system, without reducing the overall system performance. The different transmissions are tested for system nonidealities and generalizations drawn on the stability and performance margins of impedance and torque-servoed geared, cycloidal, planetary, and cable reducers in hard contact with the environment. Experimental results are furnished which underscore the validity and limitations of the theoretical modeling approach and comparative transmission analysis, while highlighting the importance of different physical system parameters necessary for proper transmission design.