The New Hot Topic:
Impedance Control –
Overview and Concepts
Max Erick Busse-Grawitz, Mar. 2018sales@electromate.com
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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
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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
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Impedance Control: Applications
Cobots
Grippers
Robots in open terrain, exoskeletons
Telemanipulation
source: EPFL
F&P robotics, source: maxon
ANYmal, source: ETH Zürich
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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
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Components: Motors
Key requirement:
 low mechanical time constant
Context dependent requirements:
 low friction
 low cogging torque
 low weight
 high torque density
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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
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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
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Components: Controllers
Controllers have to be
 fast
 fast
 fast
 well-synchronized
 compact
Examples: EPOS4 70/15 and 50/8 EtherCAT
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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
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Conclusion: Impedance Control requires
Creative
Engineering
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Questions and Remarks
Max Erick Busse-Grawitz
+41 41 666 19 45
maxerick.busse-grawitz@maxonmotor.com
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