Scaling-Based Reciprocal Control Barrier Functions for Nonholonomic Mobile Robots
arXiv:2608.22633
2026
Dynamics
1 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper offers a constructive reciprocal-barrier mechanism for constraints with relative degree two: multiplying the singular reciprocal barrier by a strictly positive, motion-dependent scaling factor can make the control appear in the first derivative of the new barrier. The transferable asset is a method for converting an otherwise uncontrollable state-margin barrier into a control-sensitive penalty or safety constraint for learned dynamical systems. A neural policy or differentiable safety layer can use the scaled barrier as a trust-region constraint in latent-state prediction, neural ODE control, or model-based reinforcement learning. The main falsifiable prediction is that control authority remains nonzero near zero constraint velocity while the barrier still diverges at the physical boundary.
Ideas from this paper
Unverified
2026
For a learned control-affine latent dynamics model, replace the ordinary reciprocal barrier 1/h₀(z) with B(z) = s(z)/h₀(z), where h₀ is the physical safety margin and s is positive but depends on a velocity-like quantity whose derivative is directly affected by the action. This preserves the singularity at h₀ = 0 while giving the policy or safety projection layer first-order action authority over the barrier derivative.
Useful6/10
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