Actuation & Control

Why this matters: Actuators are the muscles of a robot. Without precise control of these muscles, even the best planning algorithm is useless.

Introduction: Turning Electrons into Motion

The journey from "robot, walk forward" to actual walking involves converting digital commands into physical force. This is the domain of actuation and control.

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Types of Actuators

Electric Motors

The most common actuator in modern robots.

Type	Torque	Speed	Efficiency	Use Case
Brushed DC	Low	High	70-80%	Hobby robots
Brushless DC	High	Very High	85-95%	Drones, EVs
Servo	Medium	Controlled	80-90%	Arms, legs
Stepper	Medium	Low	60-70%	Precision positioning

Hydraulic Actuators

High power-to-weight ratio, but complex:

graph LR
    A[Pump] --> B[Valve]
    B --> C[Cylinder]
    C --> D[Load]
    C --> E[Sensor]
    E --> B

Used in: Boston Dynamics Atlas (original), heavy industrial robots

Pneumatic Actuators

Soft, compliant, safe for human interaction:

• Artificial muscles
• Soft grippers
• Collaborative robots

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Motor Control Fundamentals

The Control Loop

Every actuator has a control loop:

graph TD
    A[Desired Position] --> B[Controller]
    B --> C[Motor Driver]
    C --> D[Motor]
    D --> E[Encoder]
    E --> B

PID Control

The workhorse of motor control:

u(t) = Kp×e(t) + Ki×∫e(t)dt + Kd×de(t)/dt

class PIDController:
    def __init__(self, kp, ki, kd):
        self.kp, self.ki, self.kd = kp, ki, kd
        self.integral = 0
        self.prev_error = 0

    def update(self, error, dt):
        self.integral += error * dt
        derivative = (error - self.prev_error) / dt
        self.prev_error = error

        return (self.kp * error +
                self.ki * self.integral +
                self.kd * derivative)

Tuning PID

Parameter	Too Low	Too High
Kp	Slow response	Oscillation
Ki	Steady-state error	Overshoot, windup
Kd	Overshoot	Noise amplification

Ziegler-Nichols Method

1. Set Ki = Kd = 0
2. Increase Kp until oscillation
3. Record critical gain Kc and period Tc
4. Set: Kp = 0.6Kc, Ki = 1.2Kc/Tc, Kd = 0.075Kc×Tc

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Advanced Control Techniques

Impedance Control

Instead of controlling position, control the relationship between force and motion:

M×ẍ + D×ẋ + K×x = F_ext

Makes the robot feel like a spring-damper system to external forces.

Model Predictive Control (MPC)

Optimize over a horizon of future states:

def mpc_step(current_state, reference_trajectory):
    # Define optimization problem
    problem = cp.Problem(
        cp.Minimize(
            sum([stage_cost(x[t], u[t], ref[t])
                 for t in range(horizon)])
        ),
        constraints=[
            x[t+1] == dynamics(x[t], u[t]),
            u_min <= u[t] <= u_max,
            x[0] == current_state
        ]
    )
    problem.solve()
    return u[0].value  # Apply first control

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Humanoid-Specific Considerations

Compliance vs. Stiffness

Mode	When to Use	Example
High stiffness	Precise positioning	Picking up a glass
Low stiffness	Unknown environment	Opening a door
Variable	Contact transitions	Walking

Series Elastic Actuators (SEA)

Add a spring between motor and load:

Advantages:

• Better force control
• Energy storage for explosive movements
• Safer human interaction

Used in: Atlas, Digit, many research robots

Quasi-Direct Drive

Minimize gear ratio for backdrivability:

• Low friction
• High bandwidth
• Excellent force sensing

Used in: MIT Cheetah, Berkeley Blue

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Power Systems

Battery Technology

Chemistry	Energy Density	Power Density	Cycle Life
LiFePO4	Medium	Very High	2000+
Li-ion NMC	High	High	500-1000
Li-Po	High	Very High	300-500

Thermal Management

Actuators and batteries generate heat. A 30% efficiency motor operating at 500W produces 150W of heat. Plan for cooling!

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Key Takeaways

Summary

1. Electric motors dominate modern robotics
2. PID control is the foundation, but not always enough
3. Impedance control enables safe interaction
4. MPC optimizes over future trajectories
5. Compliance (SEAs, QDD) is critical for dynamic robots

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Further Reading

• Chapter 2.1: Kinematics & Dynamics
• Chapter 2.3: Locomotion & Balance
• Chapter 3.2: Control Stack