[Paper Review] The Manifold Particle Filter for State Estimation on High-dimensional Implicit Manifolds

Matthew Klingensmith, Michael C. Koval+3 more|arXiv (Cornell University)|Apr 25, 2016

Robot Manipulation and Learning24 references3 citations

TL;DR

This paper proposes an Implicit Manifold Particle Filter (IMPF) that uses a signed distance field (SDF) to represent high-dimensional contact manifolds implicitly, enabling efficient particle sampling for state estimation in robots with imperfect proprioception. The method significantly outperforms conventional particle filters in convergence speed and accuracy during persistent contact, especially in 6+ DOF robotic arms and underactuated hands.

ABSTRACT

We estimate the state a noisy robot arm and underactuated hand using an Implicit Manifold Particle Filter (MPF) informed by touch sensors. As the robot touches the world, its state space collapses to a contact manifold that we represent implicitly using a signed distance field. This allows us to extend the MPF to higher (six or more) dimensional state spaces. Earlier work (which explicitly represents the contact manifold) only shows the MPF in two or three dimensions. Through a series of experiments, we show that the implicit MPF converges faster and is more accurate than a conventional particle filter during periods of persistent contact. We present three methods of sampling the implicit contact manifold, and compare them in experiments.

Motivation & Objective

• Address the challenge of state estimation in high-dimensional robotic systems with imperfect proprioception due to mechanical play, underactuation, or sensor noise.
• Overcome particle deprivation in conventional particle filters (CPF) by enabling sampling on low-dimensional contact manifolds that have zero measure in the ambient space.
• Extend the Manifold Particle Filter (MPF) to 6+ degrees of freedom by implicitly representing the contact manifold using a signed distance field (SDF) and projection.
• Enable robust state estimation during persistent contact using tactile and proprioceptive feedback, even when joint encoders are unreliable.
• Demonstrate the method’s effectiveness in both simulated and real-world experiments on a 7-DOF arm and an underactuated 3-DOF hand.

Proposed method

• Represent the contact manifold implicitly using a signed distance field (SDF) computed from a known, static environment, avoiding explicit geometric parameterization.
• Sample particles uniformly from a region near the previous particle set in the full state space, then project them onto the contact manifold using the SDF and the manipulator’s Jacobian.
• Use constraint projection to map samples from the ambient space to the contact manifold, ensuring particles remain on the feasible set of configurations.
• Implement three sampling strategies: uniform sampling in the ambient space (MPF-Uniform), particle-based sampling (MPF-Particle), and ball-based sampling (MPF-Ball), each with different projection and resampling heuristics.
• Re-weight particles based on their proximity to the previous particle distribution to maintain temporal consistency and reduce degeneracy.
• Integrate the filter into a Bayesian estimation framework where observations from tactile sensors constrain the state to the contact manifold, updating beliefs recursively.

Experimental results

Research questions

• RQ1 Can an implicit representation of the contact manifold via a signed distance field enable effective particle sampling in high-dimensional state spaces (≥6 DOF) where explicit representations fail?
• RQ2 How does the performance of the Implicit Manifold Particle Filter (IMPF) compare to the conventional particle filter (CPF) in terms of convergence speed and estimation accuracy during persistent contact?
• RQ3 Which sampling strategy—uniform, particle-based, or ball-based—yields the most accurate and robust state estimates on the implicit contact manifold?
• RQ4 To what extent does sensor latency or bias in tactile feedback affect the stability and accuracy of the IMPF, particularly in underactuated systems?
• RQ5 Can the IMPF be effectively applied to real robotic systems with noisy proprioception, such as a 7-DOF arm with cable-driven transmission or an underactuated hand with clutch-based joints?

Key findings

• The Implicit Manifold Particle Filter (IMPF) significantly outperforms the conventional particle filter (CPF) in both simulation and real robot experiments, showing faster convergence and lower estimation error during persistent contact.
• In the 7-DOF arm experiment, MPF-Ball achieved the best performance, reducing mean error by over 50% compared to CPF and outperforming MPF-Particle and MPF-Uniform.
• For the underactuated hand, all IMPF variants (MPF-Uniform, MPF-Particle, MPF-Ball) outperformed CPF, with no significant difference among themselves due to the low-dimensional, independent kinematic chains.
• The IMPF exhibited large transients in particle distribution during contact onset, likely due to unmodeled latency in strain gauge sensors, highlighting a limitation in observation model fidelity.
• The implicit SDF-based representation enables scalable state estimation on high-dimensional manifolds without requiring explicit analytic or sample-based manifold parameterization.
• Despite potential bias from non-uniform projection of ambient-space samples onto the manifold, the IMPF maintains robust performance, suggesting the bias does not severely degrade estimation quality in tested scenarios.