Geometric Computing for Simulation-Based Robot Planning

Simulation-based robot planning is a popular approach in robotics that involves using computer simulations to plan and optimize robot motions by envisioning the outcome of generated plans before their execution in the real world. This approach offers several benefits, including the ability to evaluate multiple motion plans, reduce trial-and-error in physical experimentation, and enhance safety by identifying potential collisions and other hazards before executing a motion. Although this approach can significantly benefit robotic manipulation tasks, such simulations are still computationally expensive and may require more computing power than the robotic agents can provide. In addition, uncertainties arising from, i.e., perception or simulation models must be taken into account. Current approaches often require running simulations multiple times with varying parameters to account for these uncertainties, making real-time action planning and execution difficult. This thesis presents an accelerated geometric computation, i.e., CD methods for such simulation, precisely an algorithm based on BVHs and SIMD instruction sets. The main idea is to increase the branching factor of BVH according to available SIMD width and simultaneously test BV nodes for intersection in parallel. In addition, this thesis presents compression strategies for BVH-based CD implemented on two existing CD algorithms, namely Doptree and Boxtree. The idea is to remove redundant information from BVHs, and compress 32-bit floating points used to represent BVHs. This greatly increases the number of simultaneous simulations done in parallel by robotic agents, with most benefitting remote robots, as their computing power is often limited. Furthermore, this thesis presents an idea of benchmarking as an online service. In the literature, it is quite often that the results of proposed algorithms are difficult to replicate due to missing hardware/software and different computing configurations. Combined with the idea of using a virtual machine to safely execute user-uploaded algorithms makes it possible to safely run benchmarks as an online service. Not only are the results reproducible, but they are also comparable, as they are done within the same hardware/software configurations. Finally, this thesis investigates an idea to address uncertainties by incorporating them into simulations. The main concept is to integrate uncertainty as a a probability distribution into CD algorithms. In this sense, CD algorithms will not only report collisions but also the probability when a collision occurs. The outcome is not a simple final state of the simulation but rather a probability map reflecting a continuous distribution of final states.