Is Linear Feedback on Smoothed Dynamics Sufficient for Stabilizing Contact-Rich Plans?

TL;DR

The paper tackles stabilizing contact-rich manipulation by evaluating linear feedback on smoothed contact dynamics, focusing on whether LQR can reliably stabilize trajectories generated by smoothed models. It systematically compares SP-TrajOPT and MP-TrajOPT for robust planning and analyzes the effectiveness of offline LQR gains computed from smoothed dynamics, across extensive simulation in Drake and hardware experiments with bimanual manipulation. The key finding is that while contact smoothing aids planning, linear feedback with LQR often fails to robustly stabilize contact-rich plans, though MP-TrajOPT can enhance LQR performance when solvable. The study highlights fundamental limitations of linearization under unilateral contact and provides practical insights into when smoothing-based planning combined with local feedback can be effective, guiding future design of planners and controllers for contact-rich manipulation. All results emphasize the need to account for non-symmetric contact interactions and shape uncertainty in robust planning and feedback design.

Abstract

Designing planners and controllers for contact-rich manipulation is extremely challenging as contact violates the smoothness conditions that many gradient-based controller synthesis tools assume. Contact smoothing approximates a non-smooth system with a smooth one, allowing one to use these synthesis tools more effectively. However, applying classical control synthesis methods to smoothed contact dynamics remains relatively under-explored. This paper analyzes the efficacy of linear controller synthesis using differential simulators based on contact smoothing. We introduce natural baselines for leveraging contact smoothing to compute (a) open-loop plans robust to uncertain conditions and/or dynamics, and (b) feedback gains to stabilize around open-loop plans. Using robotic bimanual whole-body manipulation as a testbed, we perform extensive empirical experiments on over 300 trajectories and analyze why LQR seems insufficient for stabilizing contact-rich plans. The video summarizing this paper and hardware experiments is found here: https://youtu.be/HLaKi6qbwQg?si=_zCAmBBD6rGSitm9.

Figures (12)

• Figure 1: These figures show snapshots of hardware experiments using LQR and open-loop controllers under perturbations to initial conditions of cylinder. The thick and thin lines represent the desired frame at the terminal time step and the current frame of the cylinder, respectively. While LQR outperforms open-loop in this example, a more comprehensive evaluation shows that LQR generally performs poorly. The hardware experiment videos can be found https://youtu.be/HLaKi6qbwQg?si=2IucjMBtXp5Sd9Ji.
• Figure 2: Illustration of our pipeline for generating dataset. We first provide RRT with the number of reference trajectories, $N_\text{test}$, and lower- and upper-bounds of $\mathbf{x}$ and $\mathbf{v}$, denoted as $\underline{[\cdot]}$ and $\bar{[\cdot]}$, respectively. Next, RRT samples initial and desired terminal states of an object and robots and plans $N_\text{test}$ different trajectories $\{\left(\mathbf{x}^{\text{rrt}}_t, \mathbf{v}^{\text{rrt}}_t\right)^i\}_{i=1}^{N_\text{test}}$. Then, our trajectory optimizers compute $N_\text{test}$ different trajectories of the object and the robots, $\{\left(\mathbf{x}^{\text{opt}}_t, \mathbf{v}^{\text{opt}}_t\right)^i\}_{i=1}^{N_\text{test}}$ using $\{\left(\mathbf{x}^{\text{rrt}}_t, \mathbf{v}^{\text{rrt}}_t\right)^i\}_{i=1}^{N_\text{test}}$ as warm-start. Finally, given $\{\left(\mathbf{x}^{\text{opt}}_t, \mathbf{v}^{\text{opt}}_t\right)^i\}_{i=1}^{N_\text{test}}$, LQR module computes $\{\left(\mathbf{K}_t^\text{lqr}\right)^i\}_{i=1}^{N_\text{test}}$ locally.
• Figure 3: Distribution of reference trajectories generated by RRT. Left: Histograms showing the distribution of the start and end configurations of the object in the RRT-generated trajectories. The goal object configuration of $(0, 0, -\pi)$ is indicated. Right: 3D visualization of start and end object configurations of reference trajectories. While $x$ and $y$ coordinates are randomized, $\theta$ is kept constant due to the cylinder's rotational symmetry.
• Figure 4: Reference trajectories on which SP-TrajOPT ran successfully.
• Figure 5: We evaluate terminal pose tracking error $\delta_{\text{terminal}}$ of cylinder using SP-TrajOPT with / without LQR under perturbation of initial conditions. Note that cdf stands for cumulative distribution function.