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### Maxon motor ag robotic symposium presentation-impedance control overview and concepts

1. The New Hot Topic: Impedance Control – Overview and Concepts Max Erick Busse-Grawitz, Mar. 2018sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
2. Starter: Electrical Impedance P = U * I , could be written as complex numbers, so 𝑢 𝑡 ∶= 2 𝑅𝑒 𝑈 cos 𝜔𝑡 + 𝐼𝑚 𝑈 sin 𝜔𝑡 𝑖 𝑡 ∶= 2 (𝑅𝑒 𝐼 cos 𝜔𝑡 + 𝐼𝑚 𝐼 sin 𝜔𝑡 ) Then 𝑃 = 𝑈 𝐼∗ where 𝐼∗ is the complex conjugate of I Now define 𝑍 = 𝑈/𝐼, also complex In the Laplace domain with with s = jω A resistor has a real Z = R Inductor: 𝑍 𝐿 = 𝑗𝜔𝐿 Capacitor: 𝑍 𝐶 = 1 / 𝑗𝜔𝐶 sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
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4. Analogy: Mechanical Impedance 𝑃 = 𝐹 𝑣∗ 𝑍 𝑚𝑒𝑐ℎ ∶= 𝐹 / 𝑣 𝑧 𝑚𝑒𝑐ℎ ∶= 𝜕𝐹 𝜕𝑣 Damper, 𝑍 𝑚𝑒𝑐ℎ =: 𝑐 = 𝐹/𝑣 Mass: 𝑍 𝑚𝑒𝑐ℎ = 𝑗𝜔𝑚 Spring: 𝑍 𝑚𝑒𝑐ℎ = 𝑘/𝑗𝜔 Note: mechanical impedance is usually multi-dimensional, so it is a 6x6 matrix instead of a scalar sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
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7. Impedance Control: Applications Cobots Grippers Robots in open terrain, exoskeletons Telemanipulation source: EPFL F&P robotics, source: maxon ANYmal, source: ETH Zürich sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
8. Impedance Control: Concept First, get the mechanics right:  adjust mass, spring constant and damping to problem  use tendons if needed  use motors with very low inertia (read: mechanical time constant)  use springs to have a balanced «default state»  use very high efficiency gears (typically with needle bearings) with low play Then, use sensors, electronics and software (how?) source: EPFL source: ABB sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
9. Components: Motors Key requirement:  low mechanical time constant Context dependent requirements:  low friction  low cogging torque  low weight  high torque density sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
10. Components: Gears Gears for good impedance control have  low backlash  high efficiency  … and dependent on application: low noise, light weight, compactness The above traits contradict each other … resulting in a steady stream of innovation sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
11. Components: Sensors Characteristics  Fast: low energy delay  Accurate  Measure relevant quantities (not as trivial as it seems) Sensor types  fast and accurate encoders • beware of external encoders: • maybe more «accuracy» on paper but: • axle rotation yield, encoder inertia and bearing friction provie hysteresis and delay  speed sensors (tachometer)  acceleration sensors (Ferraris type)  force sensors source: Komuro robotics lab source: Christiansson et. al., IEEE trans. on robotics 2008 maxon RIO (reflective integrated optical) encoder sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
12. Components: Controllers Controllers have to be  fast  fast  fast  well-synchronized  compact Examples: EPOS4 70/15 and 50/8 EtherCAT sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
13. Examples for Sub-Systems MACCEPA = Mechanically Adjustable Compliance and Configurable Equilibrium Position Actuator SEA = Series Elastic Actuator DDRA = “Haptic Drive” = Double Differential Rheological Actuator source: Jimenez et. al., J. Mechanisms Robotics 7 (4) Apr. 2015 source: Anybotics sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
14. Conclusion: Impedance Control requires Creative Engineering sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
15. Questions and Remarks Max Erick Busse-Grawitz +41 41 666 19 45 maxerick.busse-grawitz@maxonmotor.com sales@electromate.com www.electromate.com ELECTROMATE Toll Free Phone (877) SERVO98 Toll Free Fax (877) SERV099 www.electromate.com sales@electromate.com Sold & Serviced By:
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