11 problems

Let $\mathcal{M}_1$ be a language model and $\mathcal{M}_2$ a robotics model with a shared natural-language task representation. Let $n^*$ be a shared PLT trie node and let…

A.e. nonsmooth CBF analysis conjecture. A parallel analysis should be obtainable almost everywhere for the collision and orientation-dependent cases.

Let Heuristic 2 be the renewal-based policy described for the robot example, and let the reward distribution be the particular distribution used in that example. Heuristic 2 optima…

Symmetry–flatness conjecture. Symmetry plays a role in differential flatness.

Consider the experiment in which actuators are placed on a structure and receive control signals, with the top-left actuator assigned the largest negative control signal. Actuator-…

The optimization method uses gradient updates for actuator-design variables and policy parameters, with separate learning rates for each type of variable. Actuator-design landscape…

An optimization fabric is a specification $(\mathbf{M},\mathbf{f})$ which optimizes when forced. A conservative fabric is a fabric defined by an energy-conserving equation of the f…

Let $\vec{P}=(P_1,\dotsc,P_6)$ be six points in $\mathbb{R}^3$ forming the base, and let $\vec{p}=(p_1,\ldots,p_6)$ be the platform points obtained from the preceding system. After…

Let $\vec{P}=(P_1,\dotsc,P_6)$ be six points in $\mathbb{R}^3$ forming the base, and let $\vec{p}=(p_1,\ldots,p_6)$ be the six platform points. The authors construct a system of eq…

Consider a redundant mechanical system using the proposed static optimization scheme for redundancy resolution, with configuration variables subject to joint limits and zero-dynami…

Let $x$ denote the system state, $u$ the control input, and let $x_c$ denote the configuration variables subject to joint limits. Let $r(x_c)$ be the redundancy-resolution objectiv…