[Lucas et. al.; 1977]

Contactless Spacecraft Actuation

On-Orbit Servicing

Eddy-Current Forces

Force Model

Planar Inspection

Motion Primitives

Algorithmic Design

- Inspect
- Repair
- Re-purpose
- Remove

[Sullivan,Barnhart,Hill,et.al.; Space '13]

[Choset, Knepper, Flasher, et. al; ICRA '99]

For More: [Ellery,Kreisel, Sommer; AA '08][Tweddle; GNC '11][Flores-Abad,Pham, Ulrich; PAS '14][Nguyen-Huynh, Sharf; '11]

Contactless Spacecraft Actuation

On-Orbit Servicing

Eddy-Current Forces

Force Model

Planar Inspection

Motion Primitives

Algorithmic Design

[Porter,Alinger, Sedwick, et al;
* JSR '*13]

[Shoer,Peck;
* JSR '*09]

[Wang,Schaub;
* JGCD '08*]

[Brozobohaty, Karasek, Siler, et al; NP '13]

Contactless Spacecraft Actuation

On-Orbit Servicing

Eddy-Current Forces

Force Model

Planar Inspection

Motion Primitives

Algorithmic Design

[Rem, Leest, van den Akker; IJMP '97]

[Sodano, Inman; JDSMC '08]

[Ohji,Shinkai,Amei,et.al; JMPT '07]

Focus on Robotic Inspection but ...

Many Space Applications

**
Active Detumbling
**

**Docking**
[pic:NASA]

**
Manipulation
**
[Pic:NASA]

Contactless Spacecraft Actuation

On-Orbit Servicing

Eddy-Current Forces

Force Model

Planar Inspection

Motion Primitives

Algorithmic Design

[Reinhardt, Peck; SciTech '14][Reinhardt, Peck; GNC '12]

[Paudel,Bird;IEEETM '12]

Contactless Spacecraft Actuation

On-Orbit Servicing

Eddy-Current Forces

Force Model

Planar Inspection

Motion Primitives

Algorithmic Design

[Reinhardt, Peck; JSR (Submitted)][Reinhardt, Peck; Smallsat 2014]

$$ \begin{pmatrix} I\dot{\omega} \\ m\ddot{x} \end{pmatrix} = \begin{pmatrix} -\omega^{ \times} \left( I\omega \right) \\ 0 \end{pmatrix} + \begin{bmatrix} 1 & 0 \\ 0 & R \end{bmatrix} Ju $$

$$\textbf{F}_i=\left(1-\beta_1 \right )\hat{a}_1^{\times}\hat{n} + \beta_1\hat{n}$$

$$ J = C\begin{bmatrix} d_1^{\times}\left[ \textbf{F}_1\right ]& ... & d_N^{\times} \left[\textbf{F}_N\right ] \\ \textbf{F}_1&... & \textbf{F}_N \end{bmatrix} $$

Contactless Spacecraft Actuation

On-Orbit Servicing

Eddy-Current Forces

Force Model

Planar Inspection

Motion Primitives

Algorithmic Design

[Reinhardt, Peck; IEEE Trans. Robot (Preparation)][Reinhardt, Peck; ICRA '15]

\neq

≠

Contactless Spacecraft Actuation

On-Orbit Servicing

Eddy-Current Forces

Force Model

Planar Inspection

Motion Primitives

Algorithmic Design

[Reinhardt, Knepper, Peck; IJRR. (Submitted)]

Generate Design

Generate Gains

Connect Gains

Controllable Volume

Algorithm

Human

V_a = 1.755e-10

Va=1.755e−10

V_h = 4.833e-11

Vh=4.833e−11

x_1(m)

x1(m)

x_1(m)

x1(m)

x_2(m)

x2(m)

x_2(m)

x2(m)

- Force Model
- Planar Inspection
- Motion Primitives
- Algorithmic Design

Rotation Sensing

$$\boldsymbol{\tau} \propto -c\boldsymbol{\omega} + \textbf{r} \times \boldsymbol{\omega} \times \textbf{x}$$

Lyapunov Stability

$$E = \frac{1}{2} \boldsymbol{\omega} \cdot \mathbb{I} \cdot \boldsymbol{\omega}$$ $$\dot{E} = -c\| \boldsymbol{\omega}^2 \| $$

Active Detumbling

$$E = \frac{1}{2} \boldsymbol{\omega} \cdot \mathbb{I} \cdot \boldsymbol{\omega}$$ $$\dot{E} = -c\| \boldsymbol{\omega}^2 \| -c_2 \|\boldsymbol{\omega} \| \| \boldsymbol{\omega}_m \| $$