Markovian operator improves trajectory predictions for vehicle dynamics
Markovian Dynamics Enforcer: Feasibility Preserving Correction on Learned Dynamics Manifolds
Machine LearningRobotics
Summary
Sometimes predictions about how moving things like cars will behave are wrong because they don’t follow real physical limits or rules. The researchers created a tool called MaDE that fixes these predictions after they are made, making sure they obey physical laws and constraints without needing extra information like exact control inputs. MaDE uses a mix of known physics and learned adjustments to gently nudge predictions back to realistic paths. This helps make the predictions more reliable, even if it makes the predicted positions slightly less precise.
What this means in practice
- •For vehicle trajectory prediction teams: Improve predicted vehicle paths by enforcing physical feasibility after initial prediction steps in autonomous driving or traffic modeling systems.
- •For robotics control engineers: Ensure robot motion plans respect actuator and state constraints by post-processing learned trajectories with physics-informed corrections.
Authors
Kevin Yu, Tao Guo, Constantinos Antoniou, Panagiotis Angeloudis
Abstract
Neural trajectory predictors can reach low prediction error while violating dynamics, actuator limits, or state constraints, especially when controls are unobserved and dynamics are partially specified. We introduce the Markovian Dynamics Enforcer (MaDE), a time-invariant post-hoc operator mapping state-transition proposals onto a learned feasible dynamics manifold, trained on feasible states without ground-truth controls. For each transition it infers a control and recomputes the state through a completion model of known physics plus a learned residual. It then corrects that control by gradient-based inequality reduction, so inequality satisfaction is best-effort within an iteration budget. Since every correction iterate re-enters the completion model, the returned state is dynamically consistent by construction relative to that model and the supplied previous-state anchor. MaDE drives dynamics residuals to essentially zero on fully specified simulated systems, and on an underspecified system leaves a smaller true-dynamics residual than the baselines. Designed to attach to arbitrary predictors, the frozen operator is evaluated downstream of recurrent, structured state-space, and transformer predictors. On recorded vehicle trajectories the one-step residual against a kinematic bicycle model is 0.0071 to 0.0072 for MaDE and 0.1703 to 0.1714 for raw predictors. MaDE raises average displacement error by a factor of 1.57 to 1.83.