You picked the tiny overlap of “control theory” and “aesthetics.” Predictably.

I’m going to interpret gracefulness as: smooth, low-jerk, low-effort, natural-looking, non-spasmodic behavior that still satisfies control objectives (not just “doesn’t explode”). Here are the best clusters of texts that actually build that into the formalism, not just say “and the robot should move gracefully lol.”

1. Optimal feedback control & human movement (where “grace” = minimum intervention / smoothness)

These are the most conceptually satisfying if you want a principled link between control, noise, and “elegant” behavior.

1. Todorov & Jordan, “Optimal feedback control as a theory of motor coordination” (Nat Neurosci, 2002)
   • Core idea: movements look smooth and “natural” because the brain solves a stochastic optimal feedback control problem and only corrects errors that matter for the task (“minimum intervention principle”).
   • Gracefulness emerges from cost structure + noise, not from hard-coded trajectories.
2. Scott, “Optimal feedback control and the neural basis of volitional motor control” (Nat Rev Neurosci, 2004)
   • Extends the above into neurophysiology: how cortical and cerebellar circuits implement control laws that yield fast, accurate, and smooth movements.
   • Good if you care about how biological hardware realizes “nice” control.
3. Diedrichsen, Shadmehr & Ivry, “The coordination of movement: optimal feedback control and beyond” (Trends in Cognitive Sciences, 2010)
   • Survey of OFC as a unifying theory for movement, plus hierarchical control and initiation issues.
   • Explicitly about why human movement looks so absurdly “easy” compared to what the control problem actually is.
4. Big-picture texts:
   • Kandel et al., Principles of Neural Science, motor control chapters: includes sections on optimal feedback control and how the nervous system achieves smooth, coordinated movement.
   • “Motor Control and Learning” (Schmidt & Lee et al.): not pure math, but very explicit about the progression from clumsy to smooth / fluid, tying in biomechanics, feedback, and skill acquisition.

If you want to theorize “graceful emotional/behavioral control” by analogy with motor control, those OFC papers are the right mental template.

2. Robotics & trajectory planning where “grace” is literally in the cost functional

Stuff that bakes smoothness / aesthetic criteria into the planning problem.

1. Smooth & time-optimal trajectory planning for robots (Wei, 2024)
   • Explicit tradeoffs between time optimality and smoothness metrics (jerk, acceleration constraints) for robotic arms.
   • Very much “how to make robots move fast without looking like they’re seizing.”
2. Clothoids, log-aesthetic curves & aesthetic B-splines
   • “Optimal Path Smoothing with Log-Aesthetic Curves…” (CAD’19): uses log-aesthetic curves that have monotonic curvature, minimizing bending energy & curvature variation.
   • “Optimal smooth paths based on clothoids for car-like robots”: clothoids give curvature-continuous paths that look natural and are easy to track.
   • These are basically “geometric gracefulness as a control prior”: curvature & jerk become explicit penalties.
3. Integrated motion planning & control for graceful balancing robots (Ballbot work)
   • Nagarajan et al., “Integrated motion planning and control for graceful balancing mobile robots” (IJRR): defines motion policies that produce fast, stable, human-compatible motion for a dynamically balancing platform.
   • It’s one of the few that uses “graceful” in a non-handwavy way: multi-objective design (stability, responsiveness, smoothness).