PAAMP: Polytopic Action-Set And Motion Planning for Long Horizon Dynamic Motion Planning via Mixed Integer Linear Programming

TL;DR

PAAMP tackles the challenge of long-horizon, dynamically feasible motion planning by learning Polytopic Action Sets that encapsulate trajectory families and enable reformulation as Linear Programs and Mixed Integer Linear Programs. The method combines short-horizon LP/MILP formulations with a MMMP-inspired, sequence-then-solve framework built on a Mode Adjacency Graph, guided by a volume-based heuristic to efficiently identify admissible action sequences. Experiments on a torque-limited pendulum demonstrate ultra-fast solution times and robustness, illustrating applicability to underactuated and dynamic robots such as legged and aerial systems. The work contributes a scalable, principled approach to CSPs in robotic motion planning, offering practical benefits for real-time, long-horizon control.

Abstract

Optimization methods for long-horizon, dynamically feasible motion planning in robotics tackle challenging non-convex and discontinuous optimization problems. Traditional methods often falter due to the nonlinear characteristics of these problems. We introduce a technique that utilizes learned representations of the system, known as Polytopic Action Sets, to efficiently compute long-horizon trajectories. By employing a suitable sequence of Polytopic Action Sets, we transform the long-horizon dynamically feasible motion planning problem into a Linear Program. This reformulation enables us to address motion planning as a Mixed Integer Linear Program (MILP). We demonstrate the effectiveness of a Polytopic Action-Set and Motion Planning (PAAMP) approach by identifying swing-up motions for a torque-constrained pendulum as fast as 0.75 milliseconds. This approach is well-suited for solving complex motion planning and long-horizon Constraint Satisfaction Problems (CSPs) in dynamic and underactuated systems such as legged and aerial robots.

Figures (10)

• Figure 1: $\omega \in \mathcal{S}_w$ where $n = 3$.
• Figure 2: Example trajectories $x(\cdot, \omega)$, where $\omega \in \mathcal{S}_w$.
• Figure 3: Decomposition of $\mathcal{W}$ with $n = 2$ and $m = 3$. Example solution, $\omega^*$, can be found using (\ref{['eq:subproblem1-new']}) with $\mathcal{S}_i = \mathcal{S}_1$.
• Figure 4: A sample solution with sequence $\pi {=} \{45,68,34,50\}$.
• Figure 5: Visualizing $\mathcal{X}_{fi}(x_{pre})$.