Data-Efficient Characterization of the Global Dynamics of Robot Controllers with Confidence Guarantees

This paper proposes an integration of surrogate modeling and topology to significantly reduce the amount of data required to describe the underlying global dynamics of robot controllers, including closed-box ones. A Gaussian Process (GP), trained with randomized short trajectories over the state-space, acts as a surrogate model for the underlying dynamical system. Then, a combinatorial representation is built and used to describe the dynamics in the form of a directed acyclic graph, known as {\it Morse graph}. The Morse graph is able to describe the system's attractors and their corresponding regions of attraction (\roa). Furthermore, a pointwise confidence level of the global dynamics estimation over the entire state space is provided. In contrast to alternatives, the framework does not require estimation of Lyapunov functions, alleviating the need for high prediction accuracy of the GP. The framework is suitable for data-driven controllers that do not expose an analytical model as long as Lipschitz-continuity is satisfied. The method is compared against established analytical and recent machine learning alternatives for estimating \roa s, outperforming them in data efficiency without sacrificing accuracy. Link to code: https://go.rutgers.edu/49hy35e

BITKOMO: Combining Sampling and Optimization for Fast Convergence in Optimal Motion Planning

Optimal sampling based motion planning and trajectory optimization are two competing frameworks to generate optimal motion plans. Both frameworks have complementary properties: Sampling based planners are typically slow to converge, but provide optimality guarantees. Trajectory optimizers, however, are typically fast to converge, but do not provide global optimality guarantees in nonconvex problems, e.g. scenarios with obstacles. To achieve the best of both worlds, we introduce a new planner, BITKOMO, which integrates the asymptotically optimal Batch Informed Trees (BIT*) planner with the K-Order Markov Optimization (KOMO) trajectory optimization framework. Our planner is anytime and maintains the same asymptotic optimality guarantees provided by BIT*, while also exploiting the fast convergence of the KOMO trajectory optimizer. We experimentally evaluate our planner on manipulation scenarios that involve high dimensional configuration spaces, with up to two 7-DoF manipulators, obstacles and narrow passages. BITKOMO performs better than KOMO by succeeding even when KOMO fails, and it outperforms BIT* in terms of convergence to the optimal solution.Comment: 6 pages, Accepted at IROS 202

Fast-dRRT*: Efficient Multi-Robot Motion Planning for Automated Industrial Manufacturing

We present Fast-dRRT*, a sampling-based multi-robot planner, for real-time industrial automation scenarios. Fast-dRRT* builds upon the discrete rapidly-exploring random tree (dRRT*) planner, and extends dRRT* by using pre-computed swept volumes for efficient collision detection, deadlock avoidance for partial multi-robot problems, and a simplified rewiring strategy. We evaluate Fast-dRRT* on five challenging multi-robot scenarios using two to four industrial robot arms from various manufacturers. The scenarios comprise situations involving deadlocks, narrow passages, and close proximity tasks. The results are compared against dRRT*, and show Fast-dRRT* to outperform dRRT* by up to 94% in terms of finding solutions within given time limits, while only sacrificing up to 35% on initial solution cost. Furthermore, Fast-dRRT* demonstrates resilience against noise in target configurations, and is able to solve challenging welding, and pick and place tasks with reduced computational time. This makes Fast-dRRT* a promising option for real-time motion planning in industrial automation.Comment: 7 pages, 6 figures, submitted to ICRA 202

Multilevel Motion Planning: A Fiber Bundle Formulation

Motion planning problems involving high-dimensional state spaces can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles, which allows us to concisely describe and derive novel algorithms in terms of bundle restrictions and bundle sections. Fiber bundles essentially describe lower-dimensional projections of the state space using local product spaces. Given such a structure and a corresponding admissible constraint function, we can develop highly efficient and optimal search-based motion planning methods for high-dimensional state spaces. Our contributions are the following: We first introduce the terminology of fiber bundles, in particular the notion of restrictions and sections. Second, we use the notion of restrictions and sections to develop novel multilevel motion planning algorithms, which we call QRRT* and QMP*. We show these algorithms to be probabilistically complete and almost-surely asymptotically optimal. Third, we develop a novel recursive path section method based on an L1 interpolation over path restrictions, which we use to quickly find feasible path sections. And fourth, we evaluate all novel algorithms against all available OMPL algorithms on benchmarks of eight challenging environments ranging from 21 to 100 degrees of freedom, including multiple robots and nonholonomic constraints. Our findings support the efficiency of our novel algorithms and the benefit of exploiting multilevel abstractions using the terminology of fiber bundles.Comment: Submitted to IJR

Evolvability signatures of generative encodings: beyond standard performance benchmarks

Evolutionary robotics is a promising approach to autonomously synthesize machines with abilities that resemble those of animals, but the field suffers from a lack of strong foundations. In particular, evolutionary systems are currently assessed solely by the fitness score their evolved artifacts can achieve for a specific task, whereas such fitness-based comparisons provide limited insights about how the same system would evaluate on different tasks, and its adaptive capabilities to respond to changes in fitness (e.g., from damages to the machine, or in new situations). To counter these limitations, we introduce the concept of "evolvability signatures", which picture the post-mutation statistical distribution of both behavior diversity (how different are the robot behaviors after a mutation?) and fitness values (how different is the fitness after a mutation?). We tested the relevance of this concept by evolving controllers for hexapod robot locomotion using five different genotype-to-phenotype mappings (direct encoding, generative encoding of open-loop and closed-loop central pattern generators, generative encoding of neural networks, and single-unit pattern generators (SUPG)). We observed a predictive relationship between the evolvability signature of each encoding and the number of generations required by hexapods to adapt from incurred damages. Our study also reveals that, across the five investigated encodings, the SUPG scheme achieved the best evolvability signature, and was always foremost in recovering an effective gait following robot damages. Overall, our evolvability signatures neatly complement existing task-performance benchmarks, and pave the way for stronger foundations for research in evolutionary robotics.Comment: 24 pages with 12 figures in the main text, and 4 supplementary figures. Accepted at Information Sciences journal (in press). Supplemental videos are available online at, see http://goo.gl/uyY1R