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${\tt KRAFT}$: Sampling-Based Kinodynamic Replanning and Feedback Control over Approximate, Identified Models of Vehicular Systems

Aravind Sivaramakrishnan, Sumanth Tangirala, Dhruv Metha Ramesh, Edgar Granados, Kostas E. Bekris

TL;DR

This paper aims to increase the safety and reliability of executing trajectories planned for robots with non-trivial dynamics given a light-weight, approximate dynamics model by integrating an asymptotically optimal sampling-based kinodynamic tree planner and a safety mechanism to reduce collision due to second-order dynamics.

Abstract

This paper aims to increase the safety and reliability of executing trajectories planned for robots with non-trivial dynamics given a light-weight, approximate dynamics model. Scenarios include mobile robots navigating through workspaces with imperfectly modeled surfaces and unknown friction. The proposed approach, Kinodynamic Replanning over Approximate Models with Feedback Tracking (KRAFT), integrates: (i) replanning via an asymptotically optimal sampling-based kinodynamic tree planner, with (ii) trajectory following via feedback control, and (iii) a safety mechanism to reduce collision due to second-order dynamics. The planning and control components use a rough dynamics model expressed analytically via differential equations, which is tuned via system identification (SysId) in a training environment but not the deployed one. This allows the process to be fast and achieve long-horizon reasoning during each replanning cycle. At the same time, the model still includes gaps with reality, even after SysID, in new environments. Experiments demonstrate the limitations of kinematic path planning and path tracking approaches, highlighting the importance of: (a) closing the feedback-loop also at the planning level; and (b) long-horizon reasoning, for safe and efficient trajectory execution given inaccurate models.

${\tt KRAFT}$: Sampling-Based Kinodynamic Replanning and Feedback Control over Approximate, Identified Models of Vehicular Systems

TL;DR

This paper aims to increase the safety and reliability of executing trajectories planned for robots with non-trivial dynamics given a light-weight, approximate dynamics model by integrating an asymptotically optimal sampling-based kinodynamic tree planner and a safety mechanism to reduce collision due to second-order dynamics.

Abstract

This paper aims to increase the safety and reliability of executing trajectories planned for robots with non-trivial dynamics given a light-weight, approximate dynamics model. Scenarios include mobile robots navigating through workspaces with imperfectly modeled surfaces and unknown friction. The proposed approach, Kinodynamic Replanning over Approximate Models with Feedback Tracking (KRAFT), integrates: (i) replanning via an asymptotically optimal sampling-based kinodynamic tree planner, with (ii) trajectory following via feedback control, and (iii) a safety mechanism to reduce collision due to second-order dynamics. The planning and control components use a rough dynamics model expressed analytically via differential equations, which is tuned via system identification (SysId) in a training environment but not the deployed one. This allows the process to be fast and achieve long-horizon reasoning during each replanning cycle. At the same time, the model still includes gaps with reality, even after SysID, in new environments. Experiments demonstrate the limitations of kinematic path planning and path tracking approaches, highlighting the importance of: (a) closing the feedback-loop also at the planning level; and (b) long-horizon reasoning, for safe and efficient trajectory execution given inaccurate models.
Paper Structure (8 sections, 1 theorem, 2 equations, 5 figures, 6 tables, 2 algorithms)

This paper contains 8 sections, 1 theorem, 2 equations, 5 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Statement
  4. Proposed System and Methods
  5. Offline: System Identification via Factor Graphs
  6. Online: Safe Replanning Framework
  7. Experiments
  8. Discussion

Key Result

Theorem 1

Assume a 2$^{nd}$-order system executing replanning with Tree-SBMP in a static environment where deviations between predicted and true trajectories are upper bounded by distance $\delta$. For safety, it is sufficient to compute plans $p_t(\Delta)$ followed by braking maneuvers $\gamma$ so that the

Figures (5)

  • Figure 1: (Top-Left) The initial planned tree given an analytical model. (Top-Right) Execution in MuJoCo integrating kinodynamic replanning and trajectory following. (Bottom) A similar experiment with a real MuSHR.
  • Figure 2: System identification using a factor graph for an observed trajectory $\{X_0, X_1, X_2, X_3\}$. Three types of factors are present: Prior factors for the known applied controls of constant duration $\{U_0, U_1, U_2\}$; Dynamics factors for the analytical model with unknown parameters $\rho$; and Estimation factors for each observation $Z_{i,j}$ between states $X_i$ and $X_j$.
  • Figure 3: KRAFT's online operation over different replanning cycles and integration with state estimation.
  • Figure 4: Environments with features not modeled by the planner. Goal set shown in green. Top: (L-R) Bump, Slope. Btm: (L-R) Slip, Movable.
  • Figure 5: The Boxes-Real environment as seen from the two cameras, which have some small field of view overlap in the middle. The robot's initial state is on the left side, while the desired goal state (green circle) is on the right. The planned trajectory is shown in purple.

Theorems & Definitions (2)

  • Theorem 1
  • proof