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To achieve this, we draw inspiration from equivariant convolution networks and model the path planning problem as a set of signals over grids. We demonstrate that value iteration can be treated as a linear equivariant operator, which is effectively a steerable convolution. Building upon Value Iteration Networks (VIN), we propose a new Symmetric Planning (SymPlan) framework that incorporates rotation and reflection symmetry using steerable convolution networks. We evaluate our approach on four tasks: 2D navigation, visual navigation, 2 degrees of freedom (2-DOF) configuration space manipulation, and 2-DOF workspace manipulation. Our experimental results show that our symmetric planning algorithms significantly improve training efficiency and generalization performance compared to non-equivariant baselines, including VINs and GPPN. 

Robots acting in human-scale environments must plan under uncertainty in large state–action spaces and face constantly changing reward functions as requirements and goals change. Planning under uncertainty in large state–action spaces requires hierarchical abstraction for efficient computation. We introduce a new hierarchical planning framework called Abstract Markov Decision Processes (AMDPs) that can plan in a fraction of the time needed for complex decision making in ordinary MDPs. AMDPs provide abstract states, actions, and transition dynamics in multiple layers above a base-level “flat” MDP. AMDPs decompose problems into a series of subtasks with both local reward and local transition functions used to create policies for subtasks. The resulting hierarchical planning method is independently optimal at each level of abstraction, and is recursively optimal when the local reward and transition functions are correct. We present empirical results showing significantly improved planning speed, while maintaining solution quality, in the Taxi domain and in a mobile-manipulation robotics problem. Furthermore, our approach allows specification of a decision-making model for a mobile-manipulation problem on a Turtlebot, spanning from low-level control actions operating on continuous variables all the way up through high-level object manipulation tasks. 

Robots acting in human-scale environments must plan under uncertainty in large state–action spaces and face constantly changing reward functions as requirements and goals change. Planning under uncertainty in large state–action spaces requires hierarchical abstraction for efficient computation. We introduce a new hierarchical planning framework called Abstract Markov Decision Processes (AMDPs) that can plan in a fraction of the time needed for complex decision making in ordinary MDPs. AMDPs provide abstract states, actions, and transition dynamics in multiple layers above a base-level “flat” MDP. AMDPs decompose problems into a series of subtasks with both local reward and local transition functions used to create policies for subtasks. The resulting hierarchical planning method is independently optimal at each level of abstraction, and is recursively optimal when the local reward and transition functions are correct. We present empirical results showing significantly improved planning speed, while maintaining solution quality, in the Taxi domain and in a mobile-manipulation robotics problem. Furthermore, our approach allows specification of a decision-making model for a mobile-manipulation problem on a Turtlebot, spanning from low-level control actions operating on continuous variables all the way up through high-level object manipulation tasks.