Optimize design for fundamental constraints: force, power Power breakdown Power (W) Motors 180--280 Low level electronics 10 Blind locomotion <1 Gait planner <5 Autonomy 15 • “Autonomy” requires power autonomy • Maximize range before recharge • Vision 60 total CoT 0.46—0.8, depending on terrain • Also bandwidth, transparency Minitaur: update rate 1000 Hz
Motivation: analytically-guided design Motor Motor controller Gearbox Compliant element Leg kinematics Dynamic task specification for gearbox selection e.g. [De et al (2011)] e.g. [Hollerbach (1991)] [Wensing (2017)] Huge amount of past work… 𝑢, 𝑘𝑜 , … 𝑟, 𝑑, 𝑙, … , 𝐿, 𝑅, … 𝐺, 𝐽𝐺 𝑘, 𝑏, … 𝑙𝑖 , … Platform morphology 𝑑, 𝜅, 𝜌𝑡 , 𝑚𝑡 , … e.g. [De et al (2018)]
Commonly-used motor models in robotics http://ctms.engin.umich.edu/CTMS/index.php?example= MotorSpeed§ion=SystemModeling http://www.vgt.bme.hu/info_en/research/sim/fem/1.htm Deficiencies: • only one control input • does not explain full torque output • underestimates max power/max speed Model • 𝜄 current • 𝑣 voltage • 𝐿 inductance • 𝑅 resistance • 𝑘𝑒 back-EMF constant Problems: • Brittle (hard to generalize) • No analytical insight • Time/computation intensive Analytical tractability
Controlling the three-phase model Energy balance: Set control goal: • Minimize heat • Maximize power or torque Input electrical power Joule heating Mechanical output power Transient Conventional Strategies • Feedback torque control (TC) using current sensing • Typical PI diagonal current control • Usually set Id -> 0 • Voltage control (VC) – only control Vq
New “Angle Control” – couple d,q axes for task Peak torque Peak power Vlim- constrained • Recall current dynamics • Note that where 𝜔𝑚 - rotor speed (measurement), 𝜏𝑒 - elec time const (fixed param) • Idea: use both dq axes to align with 𝑟 when ሶ 𝑥 = 0 (tune for ҧ 𝑥 equilibrium condition) := Steady state operation: [1] A. De, A. Stewart-Height, and D. E. Koditschek, “Task-Based Control and Design of a BLDC Actuator for Robotics,” IEEE Robotics and Automation Letters, vol. 4, no. 3, pp. 2393--2400, 2019.
AC disadvantage and variation with motor design Disadvantage: heat production AC advantage (peak torque ratio) vs. VC (blue) and TC (red) [1] A. De, A. Stewart-Height, and D. E. Koditschek, “Task-Based Control and Design of a BLDC Actuator for Robotics,” IEEE Robotics and Automation Letters, vol. 4, no. 3, pp. 2393--2400, 2019.
Making it relevant to robotics 1DOF experimental setup • “Inverted hopper” with stance and aerial phases • Fully instrumented with a single actuator • Showing braking trials here 𝑚 𝐽𝑚 𝜏𝑚 𝑧 Flight Stance Lower stopping time when power-constrained [1] A. De, A. Stewart-Height, and D. E. Koditschek, “Task-Based Control and Design of a BLDC Actuator for Robotics,” IEEE Robotics and Automation Letters, vol. 4, no. 3, pp. 2393--2400, 2019.
Summary • Task-based control can help get closer to fundamental limits • Use task to inform control strategy – rethink interface to motor controllers • Co-design
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