The Virtues of Laziness: Multi-Query Kinodynamic Motion Planning with Lazy Methods

TL;DR

The paper introduces LazyBoE, a multi-query kinodynamic motion planner that interleaves exploration of state and control spaces while deferring expensive dynamics simulation and collision checks through lazy propagation. It builds a discrete edge-bundle representation via Monte Carlo forward dynamics on a 7-DoF Panda arm, and uses probabilistic measures $P_{lazy\_prop}$ and $P_{collision}$ with a neighborhood radius $\\theta$ to guide lazy evaluation without sacrificing asymptotic optimality. Empirically, LazyBoE achieves substantially faster planning times, higher solution diversity, and improved success rates compared to RRT, SST variants, and BoE baselines, while maintaining comparable solution costs. The work highlights practical benefits for dynamic task planning in robotics and discusses challenges in scaling, jitter from varying control sequences, and memory constraints, proposing future directions in biased sampling, selective data loading, and application-specific edge weighting.

Abstract

In this work, we introduce LazyBoE, a multi-query method for kinodynamic motion planning with forward propagation. This algorithm allows for the simultaneous exploration of a robot's state and control spaces, thereby enabling a wider suite of dynamic tasks in real-world applications. Our contributions are three-fold: i) a method for discretizing the state and control spaces to amortize planning times across multiple queries; ii) lazy approaches to collision checking and propagation of control sequences that decrease the cost of physics-based simulation; and iii) LazyBoE, a robust kinodynamic planner that leverages these two contributions to produce dynamically-feasible trajectories. The proposed framework not only reduces planning time but also increases success rate in comparison to previous approaches.

Figures (7)

• Figure 1: Several applications motivate the need for considering dynamic constraints in motion planning. The payload transport problem requires the robot to account for the added mass at its end-effector and its effects on the inertia, Coriolis, and gravity matrices in the robot dynamics model saramago2002optimum. Similarly, liquid transport in the General Waiter Motion Problem imposes acceleration constraints on the end-effector to ensure spill-free trajectories ichnowski2022gomp. Nonprehensile actions like poking can be used to singulate target objects and require an understanding of combined robot and object dynamics pasricha2022pokerrt. In this paper, we present a method for planning robot paths while considering its dynamic constraints.
• Figure 2: Perturbing the start state of an edge $e_i \in \mathcal{E}$ (black arrow) by a maximum of $\theta$ and applying $e_i.u$ for duration $e_i.\Delta t$ results in a perturbed end state ($\hat{q}_f$). Applying multiple random perturbations for $e_i$ (grey arrows in (a), green and red arrows in (b)) allows us to estimate $e_i.P_{\text{lazy\_prop}} = Pr(\|\hat{q}_f - e_i.q_f\|_2 < \theta) = 2/4$ and $e_i.P_{\text{collision}} = 1/4$ for the provided example. We repeat this process for all edges in $\mathcal{E}$ to integrate lazy approaches to simulation and collision checking in LazyBoE.
• Figure 3: LazyBoE can lazily propagate a series of edges from $\mathcal{E}$ (shown in grey) in a way that minimizes heuristic cost. After a lazy candidate path is found (blue), a full simulation and collision check is performed along this path (green) to extend the planning tree (black). To ensure the highest rate of success when performing simulation on lazy paths, neighborhood lookup is restricted to $\theta / 2$ for lazy search to allow, in the worst case, the maximum error between the end of a simulated edge and the start of the next lazy edge to be $\theta$.
• Figure 4: Our method is able to find the first solution in less time than baseline approaches, owing to its lazy approach to simulation and collision checking. Asterisks indicate significance level when comparing our planner to the baseline methods. ns indicates no significant difference.
• Figure 5: The final solution cost, i.e., the solution with the lowest cost, for our planner is comparable to the BoE planner. Asterisks indicate significance levels.