This study investigates the impact of walking and e-hailing on the scale economies of on-demand mobility services. An analytical framework is developed to i) explicitly characterize the physical interactions between passengers and vehicles in the matching and pickup processes, and ii) derive the closed-form degree of scale economies (DSE) to quantify scale economies. The general model is then specified for conventional street-hailing and e-hailing, with and without walking before pickup and after dropoff. We show that, under a system-optimum fleet size, the market always exhibits economies of scale regardless of the matching mechanism and the walking behaviors, though the scale effect diminishes as passenger demand increases. Yet, street-hailing and e-hailing show different scale economies in their matching process. While street-hailing matching shows a constant DSE of two, e-hailing matching is more sensitive to demand and its DSE diminishes to one when passenger competition emerges. Walking, on the other hand, has mixed effects on the scale economies: while the reduced pickup and in-vehicle times bring a positive scale effect, the extra walking time and possible concentration of vacant vehicles and waiting passengers on streets negatively affect scale economies. All these analytical results are validated through agent-based simulations on Manhattan with real-life demand patterns.

Robots will increasingly operate near humans that introduce uncertainties in the motion planning problem due to their complex nature. Optimization-based planners typically avoid humans through collision avoidance chance constraints. This allows the planner to optimize performance while guaranteeing probabilistic safety. However, existing real-time methods do not consider the actual probability of collision for the planned trajectory but rather its marginalization, that is, the independent collision probabilities for each planning step and/or dynamic obstacle, resulting in conservative trajectories. To address this issue, we introduce a novel real-time capable method termed Safe Horizon MPC that explicitly constrains the joint probability of collision with all obstacles over the duration of the motion plan. This is achieved by reformulating the chance-constrained planning problem using scenario optimization and predictive control. Out of sampled realizations of human motion, we identify which cases affect the optimization. This allows us to certify the planned trajectory in real-time. Our method is less conservative than state-of-the-art approaches, applicable to arbitrary probability distributions of the obstacles’ trajectories, computationally tractable and scalable. We demonstrate our proposed approach using a mobile robot and an autonomous vehicle in an environment shared with humans.

We present a sampling-based model predictive control method that uses a generic physics simulator as the dynamical model. In particular, we propose a Model Predictive Path Integral controller (MPPI) that employs the GPU-parallelizable IsaacGym simulator to compute the forward dynamics of the robot and environment. Since the simulator implicitly defines the dynamic model, our method is readily extendable to different objects and robots, allowing one to solve complex navigation and contact-rich tasks. We demonstrate the effectiveness of this method in several simulated and real-world settings, including mobile navigation with collision avoidance, non-prehensile manipulation, and whole-body control for high-dimensional configuration spaces. This is a powerful and accessible open-source tool to solve many contact-rich motion planning tasks.

Navigating mobile robots in social environments remains a challenging task due to the intricacies of human-robot interactions. Most of the motion planners designed for crowded and dynamic environments focus on choosing the best velocity to reach the goal while avoiding collisions, but do not explicitly consider the high-level navigation behavior (avoiding through the left or right side, letting others pass or passing before others, etc.). In this work, we present a novel motion planner that incorporates topology distinct paths representing diverse navigation strategies around humans. The planner selects the topology class that imitates human behavior the best using a deep neural network model trained on real-world human motion data, ensuring socially intelligent and contextually aware navigation. Our system refines the chosen path through an optimization-based local planner in real time, ensuring seamless adherence to desired social behaviors. In this way, we decouple perception and local planning from the decision-making process. We evaluate the prediction accuracy of the network with real-world data. In addition, we assess the navigation capabilities in both simulation and a real-world platform, comparing it with other state-of-the-art planners. We demonstrate that our planner exhibits socially desirable behaviors and shows a smooth and remarkable performance.

Deployment of robots in dynamic environments requires reactive trajectory generation. While optimization-based methods, such as Model Predictive Control focus on constraint verificaction, Geometric Fabrics offer a computationally efficient way to generate trajectories that include all avoidance behaviors if the environment can be represented as a set of object primitives. Obtaining such a representation from sensor data is challenging, especially in dynamic environments. In this letter, we integrate implicit environment representations, such as Signed Distance Fields and Free Space Decomposition into the framework of Geometric Fabrics. In the process, we derive how numerical gradients can be integrated into the push and pull operations in Geometric Fabrics. Our experiments reveal that both, ground robots and robotic manipulators, can be controlled using these implicit representations. Moreover, we show that, unlike the explicit representation, implicit representations can be used in the presence of dynamic obstacles without further considerations. Finally, we demonstrate our methods in the real-world, showing the applicability of our approach in practice.

In this paper, we present an approach for fleet sizing in the context of flash delivery, a time-sensitive delivery service that requires the fulfilment of customer requests in minutes. Our approach effectively combines individual delivery requests into groups and generates optimized operational plans that can be executed by a single vehicle or autonomous robot. The groups are formed using a modified routing approach for the flash delivery problem. Combining the groups into operational plans is done by solving an integer linear problem. To evaluate the effectiveness of our approach, we compare it against three alternative methods: fixed vehicle routing, non-pooled deliveries and a strategy encouraging the pooling of requests. The results demonstrate the value of our proposed approach, showcasing its ability to optimize the fleet size and improve operational efficiency. Our experimental analysis is based on a real-world dataset provided by a Dutch retailer, allowing us to gain valuable insights into the design of flash delivery operations and to analyze the effect of the maximum allowed delay, the number of stores to pick up goods from and the employed cost functions.

For an autonomous vehicle to operate reliably within real-world traffic scenarios, it is imperative to assess the repercussions of its prospective actions by anticipating the uncertain intentions exhibited by other participants in the traffic environment. Driven by the pronounced multi-modal nature of human driving behavior, this paper presents an approach that leverages Bayesian beliefs over the distribution of potential policies of other road users to construct a novel risk-aware probabilistic motion planning framework. In particular, we propose a novel contingency planner that outputs long-term contingent plans conditioned on multiple possible intents for other actors in the traffic scene. The Bayesian belief is incorporated into the optimization cost function to influence the behavior of the short-term plan based on the likelihood of other agents' policies. Furthermore, a probabilistic risk metric is employed to fine-tune the balance between efficiency and robustness. Through a series of closed-loop safety-critical simulated traffic scenarios shared with human-driven vehicles, we demonstrate the practical efficacy of our proposed approach that can handle multi-vehicle scenarios.

Control Barrier Functions (CBFs) have proven to be an effective tool for performing safe control synthesis for nonlinear systems. However, guaranteeing safety in the presence of disturbances and input constraints for high relative degree systems is a difficult problem. In this work, we propose the Robust Policy CBF (RPCBF), a practical approach for constructing robust CBF approximations online via the estimation of a value function. We establish conditions under which the approximation qualifies as a valid CBF and demonstrate the effectiveness of the RPCBF-safety filter in simulation on a variety of high relative degree input-constrained systems. Finally, we demonstrate the benefits of our method in compensating for model errors on a hardware quadcopter platform by treating the model errors as disturbances.

Mobile manipulators operating in dynamic environments shared with humans and robots must adapt in real time to environmental changes to complete their tasks effectively. While global planning methods are effective at considering the full task scope, they lack the computational efficiency required for reactive adaptation. In contrast, local planning approaches can be executed online but are limited by their inability to account for the full task's duration. To tackle this, we propose Globally-Guided Geometric Fabrics (G3F), a framework for real-time motion generation along the full task horizon, by interleaving an optimization-based planner with a fast reactive geometric motion planner, called Geometric Fabrics (GF). The approach adapts the path and explores a multitude of acceptable target poses, while accounting for collision avoidance and the robot's physical constraints. This results in a real-time adaptive framework considering whole-body motions, where a robot operates in close proximity to other robots and humans. We validate our approach through various simulations and real-world experiments on mobile manipulators in multi-agent settings, achieving improved success rates compared to vanilla GF, Prioritized Rollout Fabrics and Model Predictive Control.

Robot navigation methods allow mobile robots to operate in applications such as warehouses or hospitals. While the environment in which the robot operates imposes requirements on its navigation behavior, most existing methods do not allow the end-user to configure the robot's behavior and priorities, possibly leading to undesirable behavior (e.g., fast driving in a hospital). We propose a novel approach to adapt robot motion behavior based on natural language instructions provided by the end-user. Our zero-shot method uses an existing Visual Language Model to interpret a user text query or an image of the environment. This information is used to generate the cost function and reconfigure the parameters of a Model Predictive Controller, translating the user's instruction to the robot's motion behavior. This allows our method to safely and effectively navigate in dynamic and challenging environments. We extensively evaluate our method's individual components and demonstrate the effectiveness of our method on a ground robot in simulation and real-world experiments, and across a variety of environments and user specifications.

Navigation Among Movable Obstacles (NAMO) poses a challenge for traditional path-planning methods when obstacles block the path, requiring push actions to reach the goal. We propose a framework that enables movability-aware planning to overcome this challenge without relying on explicit obstacle placement. Our framework integrates a global Semantic Visibility Graph and a local Model Predictive Path Integral (SVG-MPPI) approach to efficiently sample rollouts, taking into account the continuous range of obstacle movability. A physics engine is adopted to simulate the interaction result of the rollouts with the environment, and generate trajectories that minimize contact force. In qualitative and quantitative experiments, SVG-MPPI outperforms the existing paradigm that uses only binary movability for planning, achieving higher success rates with reduced cumulative contact forces. Our code is available at: https://github.com/tud-amrISVG-MPPI.

We present a vehicle system capable of navigating safely and efficiently around Vulnerable Road Users (VRUs), such as pedestrians and cyclists. The system comprises key modules for environment perception, localization and mapping, motion planning, and control, integrated into a prototype vehicle. A key innovation is a motion planner based on Topology-driven Model Predictive Control (T-MPC). The guidance layer generates multiple trajectories in parallel, each representing a distinct strategy for obstacle avoidance or non-passing. The underlying trajectory optimization constrains the joint probability of collision with VRUs under generic uncertainties. To address extraordinary situations ('edge cases') that go beyond the autonomous capabilities - such as construction zones or encounters with emergency responders - the system includes an option for remote human operation, supported by visual and haptic guidance. In simulation, our motion planner outperforms three baseline approaches in terms of safety and efficiency. We also demonstrate the full system in prototype vehicle tests on a closed track, both in autonomous and remotely operated modes.

Representing the 3D environment with instance-aware semantic and geometric information is crucial for interaction-aware robots in dynamic environments. Nevertheless, creating such a representation poses challenges due to sensor noise, instance segmentation and tracking errors, and the objects' dynamic motion. This paper introduces a novel particle-based instance-aware semantic occupancy map to tackle these challenges. Particles with an augmented instance state are used to estimate the Probability Hypothesis Density (PHD) of the objects and implicitly model the environment. Utilizing a State-augmented Sequential Monte Carlo PHD (S² MC-PHD) filter, these particles are updated to jointly estimate occupancy status, semantic, and instance IDs, mitigating noise. Additionally, a memory module is adopted to enhance the map's responsiveness to previously observed objects. Experimental results on the Virtual KITTI 2 dataset demonstrate that the proposed approach surpasses state-of-the-art methods across multiple metrics under different noise conditions. Subsequent tests using real-world data further validate the effectiveness of the proposed approach.

To efficiently deploy robotic systems in society, mobile robots must move autonomously and safely through complex environments. Nonlinear model predictive control (MPC) methods provide a natural way to find a dynamically feasible trajectory through the environment without colliding with nearby obstacles. However, the limited computation power available on typical embedded robotic systems, such as quadrotors, poses a challenge to running MPC in real time, including its most expensive tasks: constraints generation and optimization. To address this problem, we propose a novel hierarchical MPC scheme that consists of a planning and a tracking layer. The planner constructs a trajectory with a long prediction horizon at a slow rate, while the tracker ensures trajectory tracking at a relatively fast rate. We prove that the proposed framework avoids collisions and is recursively feasible. Furthermore, we demonstrate its effectiveness in simulations and lab experiments with a quadrotor that needs to reach a goal position in a complex static environment. The code is efficiently implemented on the quadrotor's embedded computer to ensure real-time feasibility. Compared to a state-of-the-art single-layer MPC formulation, this allows us to increase the planning horizon by a factor of 5, which results in significantly better performance.

Task and Motion Planning (TAMP) has made strides in complex manipulation tasks, yet the execution robustness of the planned solutions remains overlooked. In this work, we propose a method for reactive TAMP to cope with runtime uncertainties and disturbances. We combine an Active Inference planner (AIP) for adaptive high-level action selection and a novel Multi-Modal Model Predictive Path Integral controller (M3P2I) for low-level control. This results in a scheme that simultaneously adapts both high-level actions and low-level motions. The AIP generates alternative symbolic plans, each linked to a cost function for M3P2I. The latter employs a physics simulator for diverse trajectory rollouts, deriving optimal control by weighing the different samples according to their cost. This idea enables blending different robot skills for fluid and reactive plan execution, accommodating plan adjustments at both the high and low levels to cope, for instance, with dynamic obstacles or disturbances that invalidate the current plan. We have tested our approach in simulations and real-world scenarios.

We study the problem of finding statistically distinct plans for stochastic task assignment problems such as online multi-robot pickup and delivery (MRPD) when facing multiple competing objectives. In many real-world settings robot fleets do not only need to fulfil delivery requests, but also have to consider auxiliary objectives such as energy efficiency or avoiding human-centered work spaces. We pose MRPD as a multi-objective optimization problem where the goal is to find MRPD policies that yield different trade-offs between given objectives. There are two main challenges: 1) MRPD is computationally hard, which limits the number of trade-offs that can reasonably be computed, and 2) due to the random task arrivals, one needs to consider statistical variance of the objective values in addition to the average. We present an adaptive sampling algorithm that finds a set of policies which i) are approximately optimal, ii) approximate the set of all optimal solutions, and iii) are statistically distinguishable. We prove completeness and adapt a state-of-the-art MRPD solver to the multi-objective setting for three example objectives. In a series of simulation experiments we demonstrate the advantages of the proposed method compared to baseline approaches and show its robustness in a sensitivity analysis. The approach is general and could be adapted to other multi-objective task assignment and planning problems under uncertainty.

Dynamic obstacle avoidance is a popular research topic for autonomous systems, such as micro aerial vehicles and service robots. Accurately evaluating the performance of dynamic obstacle avoidance methods necessitates the establishment of a metric to quantify the environment's difficulty, a crucial aspect that remains unexplored. In this paper, we propose four metrics to measure the difficulty of dynamic environments. These metrics aim to comprehensively capture the influence of obstacles' number, size, velocity, and other factors on the difficulty. We compare the proposed metrics with existing static environment difficulty metrics and validate them through over 1.5 million trials in a customized simulator. This simulator excludes the effects of perception and control errors and supports different motion and gaze planners for obstacle avoidance. The results indicate that the survivability metric outperforms and establishes a monotonic relationship between the success rate, with a Spearman's Rank Correlation Coefficient (SRCC) of over 0.9. Specifically, for every planner, lower survivability leads to a higher success rate. This metric not only facilitates fair and comprehensive benchmarking but also provides insights for refining collision avoidance methods, thereby furthering the evolution of autonomous systems in dynamic environments.

Integrating on-demand services into public transport networks might be the best way to face the current situation in which these new technologies have increased congestion in most cities. When cooperating with on-demand services rather than competing with them, public transport would not risk losing users, and could attract some passengers from private modes thanks to an increased quality of service. This fact has engendered a growing literature discussing how to design such an integrated system. However, all of that research has imposed that on-demand mobility is to solve the so-called “last-mile problem”, serving only as a feeder that connects the exact origins/destinations with the traditional public transit network. As it induces a large number of transfers and it precludes some scale-effects to be triggered, in this paper we challenge that imposition and investigate if this is the best spatial integration strategy. To do so, we study a simplified linear city in a morning peak situation, where we propose seven different line structures, all of them combining a traditional fixed line with on-demand ride-pooling (ODRP): three direct structures, where ODRP can serve full trips, three semi-direct, where a single ODRP vehicle can serve the largest part of a trip, and a base case in which ODRP is restricted to the first and final legs only. Our results show that the base case is optimal only under very specific demand patterns, or when transfer penalties are disregarded. Our analytical approach reveals relevant operational aspects of such integrated systems: namely, that the base case can help increase directness (diminishing detours), and that ODRP can help shorten the routes of the fixed services to decrease operator costs.

The estimation of probability density functions is a fundamental problem in science and engineering. However, common methods such as kernel density estimation (KDE) have been demonstrated to lack robustness, while more complex methods have not been evaluated in multi-modal estimation problems. In this paper, we present ROME (RObust Multi-modal Estimator), a non-parametric approach for density estimation which addresses the challenge of estimating multi-modal, non-normal, and highly correlated distributions. ROME utilizes clustering to segment a multi-modal set of samples into multiple uni-modal ones and then combines simple KDE estimates obtained for individual clusters in a single multi-modal estimate. We compared our approach to state-of-the-art methods for density estimation as well as ablations of ROME, showing that it not only outperforms established methods but is also more robust to a variety of distributions. Our results demonstrate that ROME can overcome the issues of over-fitting and over-smoothing exhibited by other estimators.

Smart cameras are an essential component in surveillance and monitoring applications, and they have been typically deployed in networks of fixed camera locations. The addition of mobile cameras, mounted on robots, can overcome some of the limitations of static networks such as blind spots or back-lightning, allowing the system to gather the best information at each time by active positioning. This work presents a hybrid camera system, with static and mobile cameras, where all the cameras collaborate to observe people moving freely in the environment and efficiently visualize certain attributes from each person. Our solution combines a multi-camera distributed tracking system, to localize with precision all the people, with a control scheme that moves the mobile cameras to the best viewpoints for a specific classification task. The main contribution of this paper is a novel framework that exploits the synergies that result from the cooperation of the tracking and the control modules, obtaining a system closer to the real-world application and capable of high-level scene understanding. The static camera network provides global awareness of the control scheme to move the robots. In exchange, the mobile cameras onboard the robots provide enhanced information about the people on the scene. We perform a thorough analysis of the people monitoring application performance under different conditions thanks to the use of a photo-realistic simulation environment. Our experiments demonstrate the benefits of collaborative mobile cameras with respect to static or individual camera setups.