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Chapter VI

Learning-Based Robotics

Bridging learning-based policies with real-time robotic systems requires handling multimodal action distributions and deterministic sim-to-real domain randomization.

6.1

What is one-shot / few-shot imitation learning, and how would you apply it to a cobot task?

rating — possible

One-shot imitation learning parameterizes robot trajectories using **Dynamic Movement Primitives (DMPs)**. A single kinesthetic human demonstration is encoded as a set of non-linear differential equations:

$$\tau \dot{v} = K (g - y) - D v + \left(g - y_0\right) f(x)$$

where $f(x) = \frac{\sum w_i \psi_i(x)}{\sum \psi_i(x)} x$ is a forcing function learned via linear regression over radial basis functions $\psi_i(x)$. Adaptations to new target object poses $g_{\text{new}}$ are executed analytically by updating goal parameters in real time without retraining network weights.

6.2

Where do diffusion models fit into robotics beyond image generation?

rating — possible

Diffusion Policies represent robot action distributions $p(a|o)$ as an iterative denoising process. Unlike Gaussian MLP policies which average multiple valid grasp trajectories into an invalid middle collision path, Diffusion Policies represent multimodal distributions effectively:

$$a^{k-1} = \frac{1}{\sqrt{\alpha_k}} \left( a^k - \frac{\beta_k}{\sqrt{1 - \bar{\alpha}_k}} \epsilon_\theta(a^k, o, k) \right) + \sigma_k z$$

To run real-time at $20\text{Hz}$, policies use **DDIM sampling** (reducing denoising steps from 100 to 5) coupled with TensorRT INT8 optimization on Nvidia Jetson Orin hardware.

6.3

How would you use a genetic algorithm in a robotics context?

rating — unlikely, but keep it ready

Genetic Algorithms (GA) optimize non-differentiable trajectory parameters or controller gains in physics simulation (Isaac Gym / Gazebo). Chromosomes encode controller parameters $P = [K_p, K_i, K_d, \phi_{\text{phase}}]$. Evaluation runs 1000 parallel environments testing candidate survival against fitness function $F = -\int (e^2 + w_u u^2) dt$. Best candidates undergo **Sim-to-Real Domain Randomization** (varying ground friction $\mu \in [0.2, 1.2]$, motor payload $m \pm 30\%$, latency delay $t_{\text{delay}} \in [0, 20\text{ms}]$) before deployment to hardware.