Anirudha Majumdar

Amir Ali Ahmadi, Anirudha Majumdar, Russ Tedrake · mit

We show that for continuous time dynamical systems described by polynomial differential equations of modest degree (typically equal to three), the following decision problems which arise in numerous areas of systems and control theory cannot have a polynomial time (or even pseudo-polynomial time) algorithm unless P=NP: local attractivity of an equilibrium point, stability of an equilibrium point in the sense of Lyapunov, boundedness of trajectories, convergence of all trajectories in a ball to a given equilibrium point, existence of a quadratic Lyapunov function, invariance of a ball, invariance of a quartic semialgebraic set under linear dynamics, local collision avoidance, and existence of a stabilizing control law. We also extend our earlier NP-hardness proof of testing local asymptotic stability for polynomial vector fields to the case of trigonometric differential equations of degree four.

Sumeet Singh, Yin-Lam Chow, Anirudha Majumdar et al.

In this paper we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the cumulative cost as the objective function to be minimized. This framework is axiomatically justified in terms of time-consistency of risk assessments, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk preferences from risk-neutral (i.e., expectation) to worst case. Within this framework, we propose and analyze an online risk-sensitive MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk measures, we cast the computation of the MPC control law as a convex optimization problem amenable to real-time implementation. Simulation results are presented and discussed.

Paula Gradu, John Hallman, Daniel Suo et al.

We present an open-source library of natively differentiable physics and robotics environments, accompanied by gradient-based control methods and a benchmark-ing suite. The introduced environments allow auto-differentiation through the simulation dynamics, and thereby permit fast training of controllers. The library features several popular environments, including classical control settings from OpenAI Gym. We also provide a novel differentiable environment, based on deep neural networks, that simulates medical ventilation. We give several use-cases of new scientific results obtained using the library. This includes a medical ventilator simulator and controller, an adaptive control method for time-varying linear dynamical systems, and new gradient-based methods for control of linear dynamical systems with adversarial perturbations.

Ola Shorinwa, Zhiting Mei, Justin Lidard et al.

The remarkable performance of large language models (LLMs) in content generation, coding, and common-sense reasoning has spurred widespread integration into many facets of society. However, integration of LLMs raises valid questions on their reliability and trustworthiness, given their propensity to generate hallucinations: plausible, factually-incorrect responses, which are expressed with striking confidence. Previous work has shown that hallucinations and other non-factual responses generated by LLMs can be detected by examining the uncertainty of the LLM in its response to the pertinent prompt, driving significant research efforts devoted to quantifying the uncertainty of LLMs. This survey seeks to provide an extensive review of existing uncertainty quantification methods for LLMs, identifying their salient features, along with their strengths and weaknesses. We present existing methods within a relevant taxonomy, unifying ostensibly disparate methods to aid understanding of the state of the art. Furthermore, we highlight applications of uncertainty quantification methods for LLMs, spanning chatbot and textual applications to embodied artificial intelligence applications in robotics. We conclude with open research challenges in uncertainty quantification of LLMs, seeking to motivate future research.

Anirudha Majumdar, Mohit Sharma, Dmitry Kalashnikov et al.

Visuomotor policies trained via imitation learning are capable of performing challenging manipulation tasks, but are often extremely brittle to lighting, visual distractors, and object locations. These vulnerabilities can depend unpredictably on the specifics of training, and are challenging to expose without time-consuming and expensive hardware evaluations. We propose the problem of predictive red teaming: discovering vulnerabilities of a policy with respect to environmental factors, and predicting the corresponding performance degradation without hardware evaluations in off-nominal scenarios. In order to achieve this, we develop RoboART: an automated red teaming (ART) pipeline that (1) modifies nominal observations using generative image editing to vary different environmental factors, and (2) predicts performance under each variation using a policy-specific anomaly detector executed on edited observations. Experiments across 500+ hardware trials in twelve off-nominal conditions for visuomotor diffusion policies demonstrate that RoboART predicts performance degradation with high accuracy (less than 0.19 average difference between predicted and real success rates). We also demonstrate how predictive red teaming enables targeted data collection: fine-tuning with data collected under conditions predicted to be adverse boosts baseline performance by 2-7x.

Ola Shorinwa, Jiankai Sun, Mac Schwager et al.

We present SIREN for registration of multi-robot Gaussian Splatting (GSplat) maps, with zero access to camera poses, images, and inter-map transforms for initialization or fusion of local submaps. To realize these capabilities, SIREN harnesses the versatility and robustness of semantics in three critical ways to derive a rigorous registration pipeline for multi-robot GSplat maps. First, SIREN utilizes semantics to identify feature-rich regions of the local maps where the registration problem is better posed, eliminating the need for any initialization which is generally required in prior work. Second, SIREN identifies candidate correspondences between Gaussians in the local maps using robust semantic features, constituting the foundation for robust geometric optimization, coarsely aligning 3D Gaussian primitives extracted from the local maps. Third, this key step enables subsequent photometric refinement of the transformation between the submaps, where SIREN leverages novel-view synthesis in GSplat maps along with a semantics-based image filter to compute a high-accuracy non-rigid transformation for the generation of a high-fidelity fused map. We demonstrate the superior performance of SIREN compared to competing baselines across a range of real-world datasets, and in particular, across the most widely-used robot hardware platforms, including a manipulator, drone, and quadruped. In our experiments, SIREN achieves about 90x smaller rotation errors, 300x smaller translation errors, and 44x smaller scale errors in the most challenging scenes, where competing methods struggle. We will release the code and provide a link to the project page after the review process.

Pierre Sermanet, Anirudha Majumdar, Alex Irpan et al.

Until recently, robotics safety research was predominantly about collision avoidance and hazard reduction in the immediate vicinity of a robot. Since the advent of large vision and language models (VLMs), robots are now also capable of higher-level semantic scene understanding and natural language interactions with humans. Despite their known vulnerabilities (e.g. hallucinations or jail-breaking), VLMs are being handed control of robots capable of physical contact with the real world. This can lead to dangerous behaviors, making semantic safety for robots a matter of immediate concern. Our contributions in this paper are two fold: first, to address these emerging risks, we release the ASIMOV Benchmark, a large-scale and comprehensive collection of datasets for evaluating and improving semantic safety of foundation models serving as robot brains. Our data generation recipe is highly scalable: by leveraging text and image generation techniques, we generate undesirable situations from real-world visual scenes and human injury reports from hospitals. Secondly, we develop a framework to automatically generate robot constitutions from real-world data to steer a robot's behavior using Constitutional AI mechanisms. We propose a novel auto-amending process that is able to introduce nuances in written rules of behavior; this can lead to increased alignment with human preferences on behavior desirability and safety. We explore trade-offs between generality and specificity across a diverse set of constitutions of different lengths, and demonstrate that a robot is able to effectively reject unconstitutional actions. We measure a top alignment rate of 84.3% on the ASIMOV Benchmark using generated constitutions, outperforming no-constitution baselines and human-written constitutions. Data is available at asimov-benchmark.github.io

Lihan Zha, Apurva Badithela, Michael Zhang et al.

Generalist imitation learning policies trained on large datasets show great promise for solving diverse manipulation tasks. However, to ensure generalization to different conditions, policies need to be trained with data collected across a large set of environmental factor variations (e.g., camera pose, table height, distractors) $-$ a prohibitively expensive undertaking, if done exhaustively. We introduce a principled method for deciding what data to collect and how much to collect for each factor by constructing factored scaling curves (FSC), which quantify how policy performance varies as data scales along individual or paired factors. These curves enable targeted data acquisition for the most influential factor combinations within a given budget. We evaluate the proposed method through extensive simulated and real-world experiments, across both training-from-scratch and fine-tuning settings, and show that it boosts success rates in real-world tasks in new environments by up to 26% over existing data-collection strategies. We further demonstrate how factored scaling curves can effectively guide data collection using an offline metric, without requiring real-world evaluation at scale.

Gemini Robotics Team, Krzysztof Choromanski, Coline Devin et al.

Generative world models hold significant potential for simulating interactions with visuomotor policies in varied environments. Frontier video models can enable generation of realistic observations and environment interactions in a scalable and general manner. However, the use of video models in robotics has been limited primarily to in-distribution evaluations, i.e., scenarios that are similar to ones used to train the policy or fine-tune the base video model. In this report, we demonstrate that video models can be used for the entire spectrum of policy evaluation use cases in robotics: from assessing nominal performance to out-of-distribution (OOD) generalization, and probing physical and semantic safety. We introduce a generative evaluation system built upon a frontier video foundation model (Veo). The system is optimized to support robot action conditioning and multi-view consistency, while integrating generative image-editing and multi-view completion to synthesize realistic variations of real-world scenes along multiple axes of generalization. We demonstrate that the system preserves the base capabilities of the video model to enable accurate simulation of scenes that have been edited to include novel interaction objects, novel visual backgrounds, and novel distractor objects. This fidelity enables accurately predicting the relative performance of different policies in both nominal and OOD conditions, determining the relative impact of different axes of generalization on policy performance, and performing red teaming of policies to expose behaviors that violate physical or semantic safety constraints. We validate these capabilities through 1600+ real-world evaluations of eight Gemini Robotics policy checkpoints and five tasks for a bimanual manipulator.

Apurva Badithela, David Snyder, Lihan Zha et al.

Rapid progress in imitation learning, foundation models, and large-scale datasets has led to robot manipulation policies that generalize to a wide-range of tasks and environments. However, rigorous evaluation of these policies remains a challenge. Typically in practice, robot policies are often evaluated on a small number of hardware trials without any statistical assurances. We present SureSim, a framework to augment large-scale simulation with relatively small-scale real-world testing to provide reliable inferences on the real-world performance of a policy. Our key idea is to formalize the problem of combining real and simulation evaluations as a prediction-powered inference problem, in which a small number of paired real and simulation evaluations are used to rectify bias in large-scale simulation. We then leverage non-asymptotic mean estimation algorithms to provide confidence intervals on mean policy performance. Using physics-based simulation, we evaluate both diffusion policy and multi-task fine-tuned \(π_0\) on a joint distribution of objects and initial conditions, and find that our approach saves over \(20-25\%\) of hardware evaluation effort to achieve similar bounds on policy performance.

Pierre Sermanet, Anirudha Majumdar, Vikas Sindhwani

Given the recent rate of progress in artificial intelligence (AI) and robotics, a tantalizing question is emerging: would robots controlled by emerging AI systems be strongly aligned with human values? In this work, we propose a scalable way to probe this question by generating a benchmark spanning the key moments in 824 major pieces of science fiction literature (movies, tv, novels and scientific books) where an agent (AI or robot) made critical decisions (good or bad). We use a state-of-the-art LLM's recollection of each key moment to generate questions in similar situations, the decisions made by the agent, and alternative decisions it could have made (good or bad). We then measure an approximation of how well models align with human values on a set of human-voted answers. We also generate rules that can be automatically improved via an amendment process in order to generate the first Sci-Fi inspired constitutions for promoting ethical behavior in AIs and robots in the real world. Our first finding is that modern LLMs paired with constitutions turn out to be well-aligned with human values (95.8%), contrary to unsettling decisions typically made in Sci-Fi (only 21.2% alignment). Secondly, we find that generated constitutions substantially increase alignment compared to the base model (79.4% to 95.8%), and show resilience to an adversarial prompt setting (23.3% to 92.3%). Additionally, we find that those constitutions are among the top performers on the ASIMOV Benchmark which is derived from real-world images and hospital injury reports. Sci-Fi-inspired constitutions are thus highly aligned and applicable in real-world situations. We release SciFi-Benchmark: a large-scale dataset to advance robot ethics and safety research. It comprises 9,056 questions and 53,384 answers generated through a novel LLM-introspection process, in addition to a smaller human-labeled evaluation set.

Naman Agarwal, Elad Hazan, Anirudha Majumdar et al.

We consider the setting of iterative learning control, or model-based policy learning in the presence of uncertain, time-varying dynamics. In this setting, we propose a new performance metric, planning regret, which replaces the standard stochastic uncertainty assumptions with worst case regret. Based on recent advances in non-stochastic control, we design a new iterative algorithm for minimizing planning regret that is more robust to model mismatch and uncertainty. We provide theoretical and empirical evidence that the proposed algorithm outperforms existing methods on several benchmarks.

Udaya Ghai, David Snyder, Anirudha Majumdar et al.

We consider the problem of generating maximally adversarial disturbances for a given controller assuming only blackbox access to it. We propose an online learning approach to this problem that \emph{adaptively} generates disturbances based on control inputs chosen by the controller. The goal of the disturbance generator is to minimize \emph{regret} versus a benchmark disturbance-generating policy class, i.e., to maximize the cost incurred by the controller as well as possible compared to the best possible disturbance generator \emph{in hindsight} (chosen from a benchmark policy class). In the setting where the dynamics are linear and the costs are quadratic, we formulate our problem as an online trust region (OTR) problem with memory and present a new online learning algorithm (\emph{MOTR}) for this problem. We prove that this method competes with the best disturbance generator in hindsight (chosen from a rich class of benchmark policies that includes linear-dynamical disturbance generating policies). We demonstrate our approach on two simulated examples: (i) synthetically generated linear systems, and (ii) generating wind disturbances for the popular PX4 controller in the AirSim simulator. On these examples, we demonstrate that our approach outperforms several baseline approaches, including $H_{\infty}$ disturbance generation and gradient-based methods.

Sumeet Singh, Jonathan Lacotte, Anirudha Majumdar et al.

The literature on Inverse Reinforcement Learning (IRL) typically assumes that humans take actions in order to minimize the expected value of a cost function, i.e., that humans are risk neutral. Yet, in practice, humans are often far from being risk neutral. To fill this gap, the objective of this paper is to devise a framework for risk-sensitive IRL in order to explicitly account for a human's risk sensitivity. To this end, we propose a flexible class of models based on coherent risk measures, which allow us to capture an entire spectrum of risk preferences from risk-neutral to worst-case. We propose efficient non-parametric algorithms based on linear programming and semi-parametric algorithms based on maximum likelihood for inferring a human's underlying risk measure and cost function for a rich class of static and dynamic decision-making settings. The resulting approach is demonstrated on a simulated driving game with ten human participants. Our method is able to infer and mimic a wide range of qualitatively different driving styles from highly risk-averse to risk-neutral in a data-efficient manner. Moreover, comparisons of the Risk-Sensitive (RS) IRL approach with a risk-neutral model show that the RS-IRL framework more accurately captures observed participant behavior both qualitatively and quantitatively, especially in scenarios where catastrophic outcomes such as collisions can occur.

Anirudha Majumdar, Marco Pavone

Endowing robots with the capability of assessing risk and making risk-aware decisions is widely considered a key step toward ensuring safety for robots operating under uncertainty. But, how should a robot quantify risk? A natural and common approach is to consider the framework whereby costs are assigned to stochastic outcomes - an assignment captured by a cost random variable. Quantifying risk then corresponds to evaluating a risk metric, i.e., a mapping from the cost random variable to a real number. Yet, the question of what constitutes a "good" risk metric has received little attention within the robotics community. The goal of this paper is to explore and partially address this question by advocating axioms that risk metrics in robotics applications should satisfy in order to be employed as rational assessments of risk. We discuss general representation theorems that precisely characterize the class of metrics that satisfy these axioms (referred to as distortion risk metrics), and provide instantiations that can be used in applications. We further discuss pitfalls of commonly used risk metrics in robotics, and discuss additional properties that one must consider in sequential decision making tasks. Our hope is that the ideas presented here will lead to a foundational framework for quantifying risk (and hence safety) in robotics applications.

Amir Ali Ahmadi, Anirudha Majumdar

In a recent note [8], the author provides a counterexample to the global convergence of what his work refers to as "the DSOS and SDSOS hierarchies" for polynomial optimization problems (POPs) and purports that this refutes claims in our extended abstract [4] and slides in [3]. The goal of this paper is to clarify that neither [4], nor [3], and certainly not our full paper [5], ever defined DSOS or SDSOS hierarchies as it is done in [8]. It goes without saying that no claims about convergence properties of the hierarchies in [8] were ever made as a consequence. What was stated in [4,3] was completely different: we stated that there exist hierarchies based on DSOS and SDSOS optimization that converge. This is indeed true as we discuss in this response. We also emphasize that we were well aware that some (S)DSOS hierarchies do not converge even if their natural SOS counterparts do. This is readily implied by an example in our prior work [5], which makes the counterexample in [8] superfluous. Finally, we provide concrete counterarguments to claims made in [8] that aim to challenge the scalability improvements obtained by DSOS and SDSOS optimization as compared to sum of squares (SOS) optimization. [3] A. A. Ahmadi and A. Majumdar. DSOS and SDSOS: More tractable alternatives to SOS. Slides at the meeting on Geometry and Algebra of Linear Matrix Inequalities, CIRM, Marseille, 2013. [4] A. A. Ahmadi and A. Majumdar. DSOS and SDSOS optimization: LP and SOCP-based alternatives to sum of squares optimization. In proceedings of the 48th annual IEEE Conference on Information Sciences and Systems, 2014. [5] A. A. Ahmadi and A. Majumdar. DSOS and SDSOS optimization: more tractable alternatives to sum of squares and semidefinite optimization. arXiv:1706.02586, 2017. [8] C. Josz. Counterexample to global convergence of DSOS and SDSOS hierarchies. arXiv:1707.02964, 2017.

Anirudha Majumdar, Ram Vasudevan, Mark M. Tobenkin et al.

In this paper, we present an approach for designing feedback controllers for polynomial systems that maximize the size of the time-limited backwards reachable set (BRS). We rely on the notion of occupation measures to pose the synthesis problem as an infinite dimensional linear program (LP) and provide finite dimensional approximations of this LP in terms of semidefinite programs (SDPs). The solution to each SDP yields a polynomial control policy and an outer approximation of the largest achievable BRS. In contrast to traditional Lyapunov based approaches which are non-convex and require feasible initialization, our approach is convex and does not require any form of initialization. The resulting time-varying controllers and approximated reachable sets are well-suited for use in a trajectory library or feedback motion planning algorithm. We demonstrate the efficacy and scalability of our approach on five nonlinear systems.