We present a data driven approach to construct a library of feedback motion primitives for non-holonomic vehicles that guarantees bounded error in following arbitrarily long trajectories. This ensures that motion re-planning can be avoided as long as disturbances to the vehicle remain within a certain bound and also potentially when the obstacles are displaced within a certain bound. The library is constructed along local abstractions of the dynamics that enables addition of new motion primitives through abstraction refinement. We provide sufficient conditions for construction of such robust motion primitives for a large class of nonlinear dynamics, including commonly used models, such as the standard Reeds-Shepp model. The algorithm is applied for motion planning and control of a rover with slipping without its prior modelling. Various state-the-art motion planning approaches for carlike vehicles use the bicycle model to generate feasible trajectories for high level planning BID3 . The model is either discretized in lattice based methods or used as a heuristic for measuring distance between two states in sampling based methods such as rapidly exploring random trees (RRT) BID1 . It is then up to the low level feedback controllers of the vehicle to follow the prescribed trajectory; an overview of this group of approaches can be found in Paden et al. BID2 . This might prove a challenge in cases where the bicycle model does not resemble the actual vehicle dynamics closely enough; this may result in growing error between the prescribed trajectory and vehicles position which in turn may require trajectory re-planning BID3 . Recently, approaches such as Howard et al. BID0 and Schwarting et al. BID4 have been proposed that can incorporate the vehicle dynamics in planning to ensure collision avoidance by using model predictive control. While model predictive control can provide feasible trajectories for a large class of nonlinear models, it becomes prohibitively complex for long prediction horizons and may fall into local optima for short prediction horizons in non-convex problem settings BID5 .In this work we follow the input discretization approach similar to lattice based methods for motion planning. Instead of relying on a model, we sample from the input space similar to Howard et al. BID0 . The main contribution in this work is that we construct locally linear abstractions of the system around samples in the input space and design local feedback rules to ensure fixed upper bound on state error after applying any motion primitive considering both linearization error and initial state error. Therefore , we can guarantee bounded state error through application of the motion primitives at all times. The idea of feedback based motion primitives has also been presented in Vukosavljev et al. BID6 for multi-agent drones with omni-directional controllability; the main contrast here is that we provide a tool for construction of such motion primitives for non-holonomic vehicles. We pose an assumption we refer to as robustifiability in order to be able to synthesize such motion primitives.
We show that under some assumptions on vehicle dynamics and environment uncertainty it is possible to automatically synthesize motion primitives that do not accumulate error over time.
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