Configuration space (C-space) has played a central role in collision-free motion planning, particularly for robot manipulators. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing collision-free C-space regions with rigorous certificates due to the complexities of mapping task-space obstacles through the kinematics. In this work, we present the first to our knowledge method for generating such regions and certificates through convex optimization. Our method, called C-Iris (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parametrization of the configuration space which are guaranteed to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Our regions are generated by alternating between two convex optimization problems: (1) a simultaneous search for a maximal-volume ellipse inscribed in a given polytope and a certificate that the polytope is collision-free and (2) a maximal expansion of the polytope away from the ellipse which does not violate the certificate. The volume of the ellipse and size of the polytope are allowed to grow over several iterations while being collision-free by construction. Our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the task space, and scales to realistic problems in manipulation. We demonstrate our algorithm's ability to fill a non-trivial amount of collision-free C-space in a 3-DOF example where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa and a 12-DOF bimanual manipulator.
Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the weighted sum of the individual objectives. Solutions to this scalarized optimization problem are Pareto optimal solutions to the original multi-objective problem. However, finding an accurate representation of a Pareto front remains an important challenge. Using uniformly spaced weight vectors is often inefficient and does not provide error bounds. Thus, we address the problem of computing a finite set of weight vectors such that for any other weight vector, there exists an element in the set whose error compared to optimal is minimized. To this end, we prove fundamental properties of the optimal cost as a function of the weight vector, including its continuity and concavity. Using these, we propose an algorithm that greedily adds the weight vector least-represented by the current set, and provide bounds on the error. Finally, we illustrate that the proposed approach significantly outperforms uniformly distributed weights for different robot planning problems with varying numbers of objective functions.
In this paper we study paramertized motion planning algorithms which provide universal and flexible solutions to diverse motion planning problems. Such algorithms are intended to function under a variety of external conditions which are viewed as parameters and serve as part of the input of the algorithm. Continuing the recent paper [2], we study further the concept of parametrized topological complexity. We analyse in full detail the problem of controlling a swarm of robots in the presence of multiple obstacles in Euclidean space which served for us a natural motivating example. We present an explicit parametrized motion planning algorithm solving the motion planning problem for any number of robots and obstacles in $${\mathbb R}^d$$ . This algorithm is optimal, it has minimal possible topological complexity for any $$d\ge 3 $$ odd. Besides, we describe a modification of this algorithm which is optimal for $$d\ge 2$$ even. We also analyse the parametrized topological complexity of sphere bundles using the Stiefel - Whitney characteristic classes.
We study a class of filters -- discrete finite-state transition systems employed as incremental stream transducers -- that have application to robotics: e.g., to model combinatorial estimators and also as concise encodings of feedback plans/policies. The present paper examines their minimization problem under some new assumptions. Compared to strictly deterministic filters, allowing nondeterminism supplies opportunities for compression via re-use of states. But this paper suggests that the classic automata-theoretic concept of nondeterminism, though it affords said opportunities for reduction in state complexity, is problematic in many robotics settings. Instead, we argue for a new constrained type of nondeterminism that preserves input-output behavior for circumstances when, as for robots, causation forbids 'rewinding' of the world. We identify problem instances where compression under this constrained form of nondeterminism results in improvements over all deterministic filters. In this new setting, we examine computational complexity questions for the problem of reducing the state complexity of some given input filter. A hardness result for general deterministic input filters is presented, as well as for checking specific, narrower requirements, and some special cases. These results show that this class of nondeterminism gives problems of the same complexity class as classical nondeterminism, and the narrower questions help give a more nuanced understanding of the source of this complexity.
In this paper, we view a policy or plan as a transition system over a space of information states that reflect a robot's or other observer's perspective based on limited sensing, memory, computation, and actuation. Regardless of whether policies are obtained by learning algorithms, planning algorithms, or human insight, we want to know the limits of feasibility for given robot hardware and tasks. Toward the quest to find the best policies, we establish in a general setting that minimal information transition systems (ITSs) exist up to reasonable equivalence assumptions, and are unique under some general conditions. We then apply the theory to generate new insights into several problems, including optimal sensor fusion/filtering, solving basic planning tasks, and finding minimal representations for feasible policies.
The framework of mixed observable Markov decision processes (MOMDP) models many robotic domains in which some state variables are fully observable while others are not. In this work, we identify a significant subclass of MOMDPs defined by how actions influence the fully observable components of the state and how those, in turn, influence the partially observable components and the rewards. This unique property allows for a two-level hierarchical approach we call HIerarchical Reinforcement Learning under Mixed Observability (HILMO), which restricts partial observability to the top level while the bottom level remains fully observable, enabling higher learning efficiency. The top level produces desired goals to be reached by the bottom level until the task is solved. We further develop theoretical guarantees to show that our approach can achieve optimal and quasi-optimal behavior under mild assumptions. Empirical results on long-horizon continuous control tasks demonstrate the efficacy and efficiency of our approach in terms of improved success rate, sample efficiency, and wall-clock training time. We also deploy policies learned in simulation on a real robot.
Minimum Risk Motion Planning (MRMP) has been shown to remain NP-Hard even under the conditions that lead to the practical efficiency of sampling-based and grid-based motion planning algorithms [25]. However, the hardness proof does not eliminate the importance of finding a practical solution to this problem. In this paper we identify a parameter which directly controls the hardness of MRMP. We present experiments that suggest this parameter is small for many practical MRMPs and present an algorithm guaranteed to efficiently yield high-quality solutions whenever this parameter is small. When the parameter is large, the algorithm fails gracefully—it returns a solution with bounded suboptimality. We also explore a connection between our work and previous work on the minimum constraint removal problem (MCR).
We present an algorithm that, given a representation of a road network in lane-level detail, computes a route that minimizes the expected cost to reach a given destination. In doing so, our algorithm allows us to solve for the complex trade-offs encountered when trying to decide not just which roads to follow, but also when to change between the lanes making up these roads, in order to-for example-reduce the likelihood of missing a left exit while not unnecessarily driving in the leftmost lane. This routing problem can naturally be formulated as a Markov Decision Process (MDP), in which lane change actions have stochastic outcomes. However, MDPs are known to be time-consuming to solve in general. In this paper, we show that-under reasonable assumptions-we can use a Dijkstra-like approach to solve this stochastic problem, and benefit from its efficient O(n log n) running time. This enables an autonomous vehicle to exhibit lane-selection behavior as it efficiently plans an optimal route to its destination.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.
When deploying machine learning models in high-stakes robotics applications, the ability to detect unsafe situations is crucial. Early warning systems can provide alerts when an unsafe situation is imminent (in the absence of corrective action). To reliably improve safety, these warning systems should have a provable false negative rate; i.e. of the situations that are unsafe, fewer than $\epsilon$ will occur without an alert. In this work, we present a framework that combines a statistical inference technique known as conformal prediction with a simulator of robot/environment dynamics, in order to tune warning systems to provably achieve an $\epsilon$ false negative rate using as few as $1/\epsilon$ data points. We apply our framework to a driver warning system and a robotic grasping application, and empirically demonstrate guaranteed false negative rate while also observing low false detection (positive) rate.
The usefulness of shared-control assistive robots frequently relies on the underlying autonomous agent’s ability to infer human intentions unambiguously, often from low-dimensional and noisy signals generated by the human through a control interface. In this paper, we propose a strategy in which the autonomous agent nudges the context in which the human generates their control actions. In doing so, the autonomous agent attempts to improve its own ability to infer intent accurately, which in turn allows it to provide more accurate assistance. The contributions of this paper are three-fold. First, we introduce an interface-aware information-theoretic metric for active disambiguation that aims to characterize world states according to their potential to extract maximally intent-expressive control actions from the user. Second, we propose a turn-taking based human-autonomy interaction protocol in which the autonomous agent utilizes the disambiguation metric to help itself reduce the uncertainty of its prediction of human intent. Third, we evaluate our metric and interaction protocol both in simulation and with a 9-person human subject study. Our results suggest that disambiguation (a) helps to significantly reduce task effort, as measured by number of mode switches, task completion times, and number of turns executed by the human, and (b) enables the autonomous agent to provide accurate assistance with greater contribution to the overall control signal.
This paper introduces a partial satisfaction (PS) notion for Signal Temporal Logic (STL), finding solutions for specifications that might contain unfeasible or conflicting subformulae. We formulate the planning problem for teams of agents with robust PS of STL missions as a bi-level optimization problem. The goal is to maximize the number of subformulae satisfied with preference to larger ones that have lower depth in the syntax tree of the overall specification. The second objective is to maximize the smallest STL robustness of the feasible subformulae. First, we propose three Mixed Integer Linear Programming (MILP) methods to solve the inner level of the optimization problem, two exact and a relaxation. Then, the MILP solutions are used to find approximate solutions to the outer level optimization using a linear program. Finally, we show the performance of our methods in two multi-robot case studies: motion planning in continuous spaces, and routing for heterogeneous teams over finite graph abstractions.
We focus on decentralized navigation among multiple non-communicating agents at uncontrolled street intersections. Avoiding collisions under such settings demands nuanced implicit coordination. This is challenging to accomplish; the high dimensionality of the space of possible behavior and the lack of explicit communication among agents complicate prediction and planning. However, the structure of these domains often collapses the space of possible collective behavior into a finite set of modes. Our key insight is that enabling agents to reason about modes may enable them to coordinate implicitly via intent signals encoded in their actions. In this paper, we represent modes as low-dimensional multiagent motion primitives in a compact and interpretable fashion using the formalism of topological braids. Based on this representation, we derive a probabilistic model that maps past behavior of multiple agents to a future mode. Using this model, we design a decentralized control algorithm that treats navigation as uncertainty minimization over the space of modes. This algorithm enables agents to collectively reject unsafe intersection crossing strategies in a distributed fashion. We demonstrate our approach in a simulated four-way uncontrolled intersection. Our model is shown to reduce the frequency of collisions by over 65% against baselines explicitly reasoning in the space of trajectories, while maintaining comparable time efficiency in challenging scenarios.
We compare the resilience of four distributed robot swarm clustering algorithms to masquerade attacks launched from malicious robots within the swarm. The clustering algorithms are distributed variants of DBSCAN and k-Means that have been modified for use on a distributed robot swarm that only has access to local communication and local distance measurements. We subject these distributed variants of k-Means and DBSCAN to malicious masquerade attacks and observe how clustering performance is affected. We then modify each variant to include a distributed Intrusion Detection and Response System (IDRS) to detect malicious robots and maintain the swarm’s integrity despite an attack. We evaluate all four variants both in simulation and in a hardware testbed containing a swarm of 25 Kilobot robots. We find that centralizing data within the swarm makes the swarm more vulnerable to malicious attacks, and that distributed IDRS relying on local message passing can effectively identify malicious robots and reduce their negative effects on swarm clustering performance.
This paper presents a distributed coordination algorithm for multiple, buoyancy controlled underwater robots to achieve a moving formation in a shear flow. This work is motivated by the deployment of a swarm of ocean-going robots called Driftcam to observe the pelagic scattering layer. Driftcam horizontal motion is determined by the flow field and the vertical motion is regulated by the buoyancy control. Pairwise range measurements are available to the Driftcam network via acoustic transponders. A formation buoyancy controller is designed using the backstepping method; deviation from the desired formation is measured by a potential function. Numerical simulations illustrate the efficacy of the control algorithm and motivate ongoing and future efforts to estimate of the scattering layer density.
This paper develops a new approach to direct a set of heterogeneous agents, varying in mobility and sensing capabilities, to quickly cover a large region, say for example in the search for victims after a large-scale disaster. Given that time is of the essence, we seek to mitigate computational complexity, which normally grows exponentially as the number of agents increases. We create a new framework which reduces the planning complexity through simultaneously decomposing a target domain into sub-regions, and assigning a team of agents to each sub-region in the target domain, as a way to decompose a large-scale problem into a set of smaller problems. The teams are formed to optimize the coverage of each sub-regions. Doing so requires both the utilization of individual agents’ strengths as well as their collaborative capabilities. We determine the ideal team by introducing a novel evolution-guided generative model based on generative adversarial networks (GANs) that creates allocation plans from the sub-region features in a computationally efficient manner. We validate our framework on a real-world satellite images dataset, and demonstrate that through decomposition and generative allocation, our method has significantly better efficiency and efficacy compared to current centralized multi-robot coverage methods, and is therefore better suited for large-scale time-critical deployment.
Motion Planning is widely acknowledged as a fundamental problem of robotics. Due to the continuous efforts of the scientific community, various algorithmic families emerged that have different strengths and weaknesses. Finding a suitable motion planning program is often not trivial for real-world problems, as various domain-specific factors must be considered. An obvious example is a potential trade-off between path length, computation time, and resource constraints. We propose a technique to systematically explore the space of suitable programs, aiming to find Pareto optimal algorithm configurations. Our approach makes use of Combinatory Logic Synthesis to perform component-based software composition. Software components are injected with domain-knowledge, effectively restricting the solution space of synthesizable programs. We synthesize sample-based global planning programs that make use of the Open Motion Planning Library (OMPL) and evaluate the produced programs to yield numeric result vectors. These steps are encapsulated in a black-box function which is used with a multi-objective optimization tool (Hypermapper) to yield an automatic, learning-based search procedure for a given feature space. We validate our approach with a series of experiments that demonstrate the extensibility and transferability of our methodology regarding different robotic systems and planning instances.
Proving motion planning infeasibility is an important part of a complete motion planner. Common approaches for high-dimensional motion planning are only probabilistically complete. Previously, we presented an algorithm to construct infeasibility proofs by applying machine learning to sampled configurations from a bidirectional sampling-based planner. In this work, we prove that the learned manifold converges to an infeasibility proof exponentially. Combining prior approaches for sampling-based planning and our converging infeasibility proofs, we propose the term asymptotic completeness to describe the property of returning a plan or infeasibility proof in the limit. We compare the empirical convergence of different sampling strategies to validate our analysis.
We present a novel method for extracting geometric and topological features from a robot’s configuration space. To accomplish this, we define a discrete Morse function on the Vietoris-Rips simplicial complex to identify critical points on the surface of obstacles present. These critical points serve as waypoints for determining feasible bounds near an identified obstacle. This work builds on previous work that provides a method to approximate the number of samples required to generate pathways. Our results achieve near-optimal paths with a low computation time and reduced path distance in this work. We conduct experiments in different environments and with various robots, including the Kuka YouBot and PR2 robots in simulation, and demonstrate the performance gains compared to state-of-the-art methods.
