Control Barrier Functions for Safety-Aware Latent-Space Motion Planning

Abstract

Latent-space path planning (LSPP) compresses the configuration space of a robotic manipulator into a compact, differentiable manifold learned by a variational autoencoder, enabling fast gradient-based planning without explicit inverse kinematics. Existing LSPP frameworks enforce obstacle avoidance with a binary collision classifier, whose saturated gradients near obstacle boundaries and lack of temporal structure cause the optimizer to stall and provide no forward-invariance guarantee. We replace the classifier with a neural control barrier function (CBF) learned directly in the latent space. The barrier is trained with a three-term objective that combines safe and unsafe sign constraints with a discrete-time decrease condition evaluated on transitions of an obstacle-blind nominal planner, and it is enforced at planning time by a closed-form, first-order correction that projects each goal-directed latent step back onto the CBF constraint. On a 7-DoF Franka Panda manipulator, the CBF planner achieves a 75.6\% success rate on a fixed-obstacle task, 12.0 percentage points above the best of 35 tuned classifier configurations, and 83.8\% on a multi-position task. A sweep of the decay rate $α$ characterizes the safety--performance trade-off, with the best operating points in $α\in [0.10, 0.20]$. In a fully general random-obstacle setting, success drops to 33.0\%, which we trace to covariate shift between the obstacle-blind training transitions and the states visited by the corrected planner.