Madhava Krishna

Krishna Murthy Jatavallabhula, Alihusein Kuwajerwala, Qiao Gu et al. · deepmind, mit

Building 3D maps of the environment is central to robot navigation, planning, and interaction with objects in a scene. Most existing approaches that integrate semantic concepts with 3D maps largely remain confined to the closed-set setting: they can only reason about a finite set of concepts, pre-defined at training time. Further, these maps can only be queried using class labels, or in recent work, using text prompts. We address both these issues with ConceptFusion, a scene representation that is (1) fundamentally open-set, enabling reasoning beyond a closed set of concepts and (ii) inherently multimodal, enabling a diverse range of possible queries to the 3D map, from language, to images, to audio, to 3D geometry, all working in concert. ConceptFusion leverages the open-set capabilities of today's foundation models pre-trained on internet-scale data to reason about concepts across modalities such as natural language, images, and audio. We demonstrate that pixel-aligned open-set features can be fused into 3D maps via traditional SLAM and multi-view fusion approaches. This enables effective zero-shot spatial reasoning, not needing any additional training or finetuning, and retains long-tailed concepts better than supervised approaches, outperforming them by more than 40% margin on 3D IoU. We extensively evaluate ConceptFusion on a number of real-world datasets, simulated home environments, a real-world tabletop manipulation task, and an autonomous driving platform. We showcase new avenues for blending foundation models with 3D open-set multimodal mapping. For more information, visit our project page https://concept-fusion.github.io or watch our 5-minute explainer video https://www.youtube.com/watch?v=rkXgws8fiDs

Nikhil Keetha, Avneesh Mishra, Jay Karhade et al. · mit

Visual Place Recognition (VPR) is vital for robot localization. To date, the most performant VPR approaches are environment- and task-specific: while they exhibit strong performance in structured environments (predominantly urban driving), their performance degrades severely in unstructured environments, rendering most approaches brittle to robust real-world deployment. In this work, we develop a universal solution to VPR -- a technique that works across a broad range of structured and unstructured environments (urban, outdoors, indoors, aerial, underwater, and subterranean environments) without any re-training or fine-tuning. We demonstrate that general-purpose feature representations derived from off-the-shelf self-supervised models with no VPR-specific training are the right substrate upon which to build such a universal VPR solution. Combining these derived features with unsupervised feature aggregation enables our suite of methods, AnyLoc, to achieve up to 4X significantly higher performance than existing approaches. We further obtain a 6% improvement in performance by characterizing the semantic properties of these features, uncovering unique domains which encapsulate datasets from similar environments. Our detailed experiments and analysis lay a foundation for building VPR solutions that may be deployed anywhere, anytime, and across anyview. We encourage the readers to explore our project page and interactive demos: https://anyloc.github.io/.

Kartik Garg, Sai Shubodh Puligilla, Shishir Kolathaya et al.

Accurately recognizing a revisited place is crucial for embodied agents to localize and navigate. This requires visual representations to be distinct, despite strong variations in camera viewpoint and scene appearance. Existing visual place recognition pipelines encode the "whole" image and search for matches. This poses a fundamental challenge in matching two images of the same place captured from different camera viewpoints: "the similarity of what overlaps can be dominated by the dissimilarity of what does not overlap". We address this by encoding and searching for "image segments" instead of the whole images. We propose to use open-set image segmentation to decompose an image into `meaningful' entities (i.e., things and stuff). This enables us to create a novel image representation as a collection of multiple overlapping subgraphs connecting a segment with its neighboring segments, dubbed SuperSegment. Furthermore, to efficiently encode these SuperSegments into compact vector representations, we propose a novel factorized representation of feature aggregation. We show that retrieving these partial representations leads to significantly higher recognition recall than the typical whole image based retrieval. Our segments-based approach, dubbed SegVLAD, sets a new state-of-the-art in place recognition on a diverse selection of benchmark datasets, while being applicable to both generic and task-specialized image encoders. Finally, we demonstrate the potential of our method to ``revisit anything'' by evaluating our method on an object instance retrieval task, which bridges the two disparate areas of research: visual place recognition and object-goal navigation, through their common aim of recognizing goal objects specific to a place. Source code: https://github.com/AnyLoc/Revisit-Anything.

Bipasha Sen, Aditya Agarwal, Gaurav Singh et al. · mila, mit

Recovering full 3D shapes from partial observations is a challenging task that has been extensively addressed in the computer vision community. Many deep learning methods tackle this problem by training 3D shape generation networks to learn a prior over the full 3D shapes. In this training regime, the methods expect the inputs to be in a fixed canonical form, without which they fail to learn a valid prior over the 3D shapes. We propose SCARP, a model that performs Shape Completion in ARbitrary Poses. Given a partial pointcloud of an object, SCARP learns a disentangled feature representation of pose and shape by relying on rotationally equivariant pose features and geometric shape features trained using a multi-tasking objective. Unlike existing methods that depend on an external canonicalization, SCARP performs canonicalization, pose estimation, and shape completion in a single network, improving the performance by 45% over the existing baselines. In this work, we use SCARP for improving grasp proposals on tabletop objects. By completing partial tabletop objects directly in their observed poses, SCARP enables a SOTA grasp proposal network improve their proposals by 71.2% on partial shapes. Project page: https://bipashasen.github.io/scarp

Rohith Agaram, Shaurya Dewan, Rahul Sajnani et al. · stanford

Coordinate-based implicit neural networks, or neural fields, have emerged as useful representations of shape and appearance in 3D computer vision. Despite advances, however, it remains challenging to build neural fields for categories of objects without datasets like ShapeNet that provide "canonicalized" object instances that are consistently aligned for their 3D position and orientation (pose). We present Canonical Field Network (CaFi-Net), a self-supervised method to canonicalize the 3D pose of instances from an object category represented as neural fields, specifically neural radiance fields (NeRFs). CaFi-Net directly learns from continuous and noisy radiance fields using a Siamese network architecture that is designed to extract equivariant field features for category-level canonicalization. During inference, our method takes pre-trained neural radiance fields of novel object instances at arbitrary 3D pose and estimates a canonical field with consistent 3D pose across the entire category. Extensive experiments on a new dataset of 1300 NeRF models across 13 object categories show that our method matches or exceeds the performance of 3D point cloud-based methods.

Kallol Saha, Vishal Mandadi, Jayaram Reddy et al. · mila, mit

Classical motion planning for robotic manipulation includes a set of general algorithms that aim to minimize a scene-specific cost of executing a given plan. This approach offers remarkable adaptability, as they can be directly used off-the-shelf for any new scene without needing specific training datasets. However, without a prior understanding of what diverse valid trajectories are and without specially designed cost functions for a given scene, the overall solutions tend to have low success rates. While deep-learning-based algorithms tremendously improve success rates, they are much harder to adopt without specialized training datasets. We propose EDMP, an Ensemble-of-costs-guided Diffusion for Motion Planning that aims to combine the strengths of classical and deep-learning-based motion planning. Our diffusion-based network is trained on a set of diverse kinematically valid trajectories. Like classical planning, for any new scene at the time of inference, we compute scene-specific costs such as "collision cost" and guide the diffusion to generate valid trajectories that satisfy the scene-specific constraints. Further, instead of a single cost function that may be insufficient in capturing diversity across scenes, we use an ensemble of costs to guide the diffusion process, significantly improving the success rate compared to classical planners. EDMP performs comparably with SOTA deep-learning-based methods while retaining the generalization capabilities primarily associated with classical planners.

Nandiraju Gireesh, D. A. Sasi Kiran, Snehasis Banerjee et al.

Object Goal Navigation requires a robot to find and navigate to an instance of a target object class in a previously unseen environment. Our framework incrementally builds a semantic map of the environment over time, and then repeatedly selects a long-term goal ('where to go') based on the semantic map to locate the target object instance. Long-term goal selection is formulated as a vision-based deep reinforcement learning problem. Specifically, an Encoder Network is trained to extract high-level features from a semantic map and select a long-term goal. In addition, we incorporate data augmentation and Q-function regularization to make the long-term goal selection more effective. We report experimental results using the photo-realistic Gibson benchmark dataset in the AI Habitat 3D simulation environment to demonstrate substantial performance improvement on standard measures in comparison with a state of the art data-driven baseline.

D. A. Sasi Kiran, Kritika Anand, Chaitanya Kharyal et al.

This paper describes a framework for the object-goal navigation task, which requires a robot to find and move to the closest instance of a target object class from a random starting position. The framework uses a history of robot trajectories to learn a Spatial Relational Graph (SRG) and Graph Convolutional Network (GCN)-based embeddings for the likelihood of proximity of different semantically-labeled regions and the occurrence of different object classes in these regions. To locate a target object instance during evaluation, the robot uses Bayesian inference and the SRG to estimate the visible regions, and uses the learned GCN embeddings to rank visible regions and select the region to explore next.

Madhava Krishna, A V Subramanyam

SimMIM is a widely used method for pretraining vision transformers using masked image modeling. However, despite its success in fine-tuning performance, it has been shown to perform sub-optimally when used for linear probing. We propose an efficient patch-wise weighting derived from keypoint features which captures the local information and provides better context during SimMIM's reconstruction phase. Our method, KAMIM, improves the top-1 linear probing accuracy from 16.12% to 33.97%, and finetuning accuracy from 76.78% to 77.3% when tested on the ImageNet-1K dataset with a ViT-B when trained for the same number of epochs. We conduct extensive testing on different datasets, keypoint extractors, and model architectures and observe that patch-wise weighting augments linear probing performance for larger pretraining datasets. We also analyze the learned representations of a ViT-B trained using KAMIM and observe that they behave similar to contrastive learning with regard to its behavior, with longer attention distances and homogenous self-attention across layers. Our code is publicly available at https://github.com/madhava20217/KAMIM.

Vansh Garg, Rohit Jayanti, Krish Pandya et al.

Visual navigation ability is strongly tied to its underlying representation of the world. Unlike classical 3D maps that require globally-consistent geometry, image- or object-relative topological graphs almost entirely do away with geometric understanding. But, this comes at the cost of navigation capability, often limiting it to merely teach-and-repeat. In this work, we propose a novel map representation in the form of pixel-relative connectivity, which is geometrically accurate but does not require global geometric consistency. Inspired by recent progress in 3D grounded image matching, we construct a map from an image sequence through inter-image connectivity based on pixel correspondences in the relative 3D coordinate systems of individual image pairs. We then use this pixel-level graph to perform global path planning by approximating and sparsifying intra-image pixel connectivity. Through this, we derive a ''WayPixel Costmap'' representation and train a controller conditioned on it to predict a trajectory rollout. We show that this dense pixel-level costmap based on relative geometry is a more accurate conditioning variable for control prediction than its image- and object-level counterparts. This enables a highly capable navigation system, as validated on four types of navigation tasks in the simulator and through real world demonstrations.

Autrio Das, Shreya Bollimuntha, Madala Venkata Renu Jeevesh et al.

What appears effortless to a human waiter remains a major challenge for robots. Manipulating objects nonprehensilely on a tray is inherently difficult, and the complexity is amplified in dual-arm settings. Such tasks are highly relevant to service robotics in domains such as hotels and hospitality, where robots must transport and reposition diverse objects with precision. We present DART, a novel dual-arm framework that integrates nonlinear Model Predictive Control (MPC) with an optimization-based impedance controller to achieve accurate object motion relative to a dynamically controlled tray. The framework systematically evaluates three complementary strategies for modeling tray-object dynamics as the state transition function within our MPC formulation: (i) a physics-based analytical model, (ii) an online regression based identification model that adapts in real-time, and (iii) a reinforcement learning-based dynamics model that generalizes across object properties. Our pipeline is validated in simulation with objects of varying mass, geometry, and friction coefficients. Extensive evaluations highlight the trade-offs among the three modeling strategies in terms of settling time, steady-state error, control effort, and generalization across objects. To the best of our knowledge, DART constitutes the first framework for non-prehensile dual-arm manipulation of objects on a tray. Project Link: https://dart-icra.github.io/dart/

Madhava Krishna, Bhagesh Gaur, Arsh Verma et al.

The creation of a Software Requirements Specification (SRS) document is important for any software development project. Given the recent prowess of Large Language Models (LLMs) in answering natural language queries and generating sophisticated textual outputs, our study explores their capability to produce accurate, coherent, and structured drafts of these documents to accelerate the software development lifecycle. We assess the performance of GPT-4 and CodeLlama in drafting an SRS for a university club management system and compare it against human benchmarks using eight distinct criteria. Our results suggest that LLMs can match the output quality of an entry-level software engineer to generate an SRS, delivering complete and consistent drafts. We also evaluate the capabilities of LLMs to identify and rectify problems in a given requirements document. Our experiments indicate that GPT-4 is capable of identifying issues and giving constructive feedback for rectifying them, while CodeLlama's results for validation were not as encouraging. We repeated the generation exercise for four distinct use cases to study the time saved by employing LLMs for SRS generation. The experiment demonstrates that LLMs may facilitate a significant reduction in development time for entry-level software engineers. Hence, we conclude that the LLMs can be gainfully used by software engineers to increase productivity by saving time and effort in generating, validating and rectifying software requirements.

Sai Shubodh Puligilla, Mohammad Omama, Husain Zaidi et al.

Global visual localization in LiDAR-maps, crucial for autonomous driving applications, remains largely unexplored due to the challenging issue of bridging the cross-modal heterogeneity gap. Popular multi-modal learning approach Contrastive Language-Image Pre-Training (CLIP) has popularized contrastive symmetric loss using batch construction technique by applying it to multi-modal domains of text and image. We apply this approach to the domains of 2D image and 3D LiDAR points on the task of cross-modal localization. Our method is explained as follows: A batch of N (image, LiDAR) pairs is constructed so as to predict what is the right match between N X N possible pairings across the batch by jointly training an image encoder and LiDAR encoder to learn a multi-modal embedding space. In this way, the cosine similarity between N positive pairings is maximized, whereas that between the remaining negative pairings is minimized. Finally, over the obtained similarity scores, a symmetric cross-entropy loss is optimized. To the best of our knowledge, this is the first work to apply batched loss approach to a cross-modal setting of image & LiDAR data and also to show Zero-shot transfer in a visual localization setting. We conduct extensive analyses on standard autonomous driving datasets such as KITTI and KITTI-360 datasets. Our method outperforms state-of-the-art recall@1 accuracy on the KITTI-360 dataset by 22.4%, using only perspective images, in contrast to the state-of-the-art approach, which utilizes the more informative fisheye images. Additionally, this superior performance is achieved without resorting to complex architectures. Moreover, we demonstrate the zero-shot capabilities of our model and we beat SOTA by 8% without even training on it. Furthermore, we establish the first benchmark for cross-modal localization on the KITTI dataset.

Raghav Arora, Shivam Singh, Karthik Swaminathan et al. · mit

Assistive agents performing household tasks such as making the bed or cooking breakfast often compute and execute actions that accomplish one task at a time. However, efficiency can be improved by anticipating upcoming tasks and computing an action sequence that jointly achieves these tasks. State-of-the-art methods for task anticipation use data-driven deep networks and Large Language Models (LLMs), but they do so at the level of high-level tasks and/or require many training examples. Our framework leverages the generic knowledge of LLMs through a small number of prompts to perform high-level task anticipation, using the anticipated tasks as goals in a classical planning system to compute a sequence of finer-granularity actions that jointly achieve these goals. We ground and evaluate our framework's abilities in realistic scenarios in the VirtualHome environment and demonstrate a 31% reduction in execution time compared with a system that does not consider upcoming tasks.

Yash Mehan, Kumaraditya Gupta, Rohit Jayanti et al.

Robotic tasks such as planning and navigation require a hierarchical semantic understanding of a scene, which could include multiple floors and rooms. Current methods primarily focus on object segmentation for 3D scene understanding. However, such methods struggle to segment out topological regions like "kitchen" in the scene. In this work, we introduce a two-step pipeline to solve this problem. First, we extract a topological map, i.e., floorplan of the indoor scene using a novel multi-channel occupancy representation. Then, we generate CLIP-aligned features and semantic labels for every room instance based on the objects it contains using a self-attention transformer. Our language-topology alignment supports natural language querying, e.g., a "place to cook" locates the "kitchen". We outperform the current state-of-the-art on room segmentation by ~20% and room classification by ~12%. Our detailed qualitative analysis and ablation studies provide insights into the problem of joint structural and semantic 3D scene understanding. Project Page: quest-maps.github.io

Shivam Singh, Karthik Swaminathan, Nabanita Dash et al.

An embodied agent assisting humans is often asked to complete new tasks, and there may not be sufficient time or labeled examples to train the agent to perform these new tasks. Large Language Models (LLMs) trained on considerable knowledge across many domains can be used to predict a sequence of abstract actions for completing such tasks, although the agent may not be able to execute this sequence due to task-, agent-, or domain-specific constraints. Our framework addresses these challenges by leveraging the generic predictions provided by LLM and the prior domain knowledge encoded in a Knowledge Graph (KG), enabling an agent to quickly adapt to new tasks. The robot also solicits and uses human input as needed to refine its existing knowledge. Based on experimental evaluation in the context of cooking and cleaning tasks in simulation domains, we demonstrate that the interplay between LLM, KG, and human input leads to substantial performance gains compared with just using the LLM. Project website§: https://sssshivvvv.github.io/adaptbot/

Sourav Garg, Dustin Craggs, Vineeth Bhat et al.

Visual navigation using only a single camera and a topological map has recently become an appealing alternative to methods that require additional sensors and 3D maps. This is typically achieved through an "image-relative" approach to estimating control from a given pair of current observation and subgoal image. However, image-level representations of the world have limitations because images are strictly tied to the agent's pose and embodiment. In contrast, objects, being a property of the map, offer an embodiment- and trajectory-invariant world representation. In this work, we present a new paradigm of learning "object-relative" control that exhibits several desirable characteristics: a) new routes can be traversed without strictly requiring to imitate prior experience, b) the control prediction problem can be decoupled from solving the image matching problem, and c) high invariance can be achieved in cross-embodiment deployment for variations across both training-testing and mapping-execution settings. We propose a topometric map representation in the form of a "relative" 3D scene graph, which is used to obtain more informative object-level global path planning costs. We train a local controller, dubbed "ObjectReact", conditioned directly on a high-level "WayObject Costmap" representation that eliminates the need for an explicit RGB input. We demonstrate the advantages of learning object-relative control over its image-relative counterpart across sensor height variations and multiple navigation tasks that challenge the underlying spatial understanding capability, e.g., navigating a map trajectory in the reverse direction. We further show that our sim-only policy is able to generalize well to real-world indoor environments. Code and supplementary material are accessible via project page: https://object-react.github.io/

Siddharth Tourani, Jayaram Reddy, Akash Kumbar et al.

Dynamic scene rendering and reconstruction play a crucial role in computer vision and augmented reality. Recent methods based on 3D Gaussian Splatting (3DGS), have enabled accurate modeling of dynamic urban scenes, but for urban scenes they require both camera and LiDAR data, ground-truth 3D segmentations and motion data in the form of tracklets or pre-defined object templates such as SMPL. In this work, we explore whether a combination of 2D object agnostic priors in the form of depth and point tracking coupled with a signed distance function (SDF) representation for dynamic objects can be used to relax some of these requirements. We present a novel approach that integrates Signed Distance Functions (SDFs) with 3D Gaussian Splatting (3DGS) to create a more robust object representation by harnessing the strengths of both methods. Our unified optimization framework enhances the geometric accuracy of 3D Gaussian splatting and improves deformation modeling within the SDF, resulting in a more adaptable and precise representation. We demonstrate that our method achieves state-of-the-art performance in rendering metrics even without LiDAR data on urban scenes. When incorporating LiDAR, our approach improved further in reconstructing and generating novel views across diverse object categories, without ground-truth 3D motion annotation. Additionally, our method enables various scene editing tasks, including scene decomposition, and scene composition.

Rohit Jayanti, Swayam Agrawal, Vansh Garg et al.

Segment matching is an important intermediate task in computer vision that establishes correspondences between semantically or geometrically coherent regions across images. Unlike keypoint matching, which focuses on localized features, segment matching captures structured regions, offering greater robustness to occlusions, lighting variations, and viewpoint changes. In this paper, we leverage the spatial understanding of 3D foundation models to tackle wide-baseline segment matching, a challenging setting involving extreme viewpoint shifts. We propose an architecture that uses the inductive bias of these 3D foundation models to match segments across image pairs with up to 180 degree view-point change rotation. Extensive experiments show that our approach outperforms state-of-the-art methods, including the SAM2 video propagator and local feature matching methods, by up to 30% on the AUPRC metric, on ScanNet++ and Replica datasets. We further demonstrate benefits of the proposed model on relevant downstream tasks, including 3D instance mapping and object-relative navigation. Project Page: https://segmast3r.github.io/

Shivam Singh, Karthik Swaminathan, Raghav Arora et al.

An agent assisting humans in daily living activities can collaborate more effectively by anticipating upcoming tasks. Data-driven methods represent the state of the art in task anticipation, planning, and related problems, but these methods are resource-hungry and opaque. Our prior work introduced a proof of concept framework that used an LLM to anticipate 3 high-level tasks that served as goals for a classical planning system that computed a sequence of low-level actions for the agent to achieve these goals. This paper describes DaTAPlan, our framework that significantly extends our prior work toward human-robot collaboration. Specifically, DaTAPlan planner computes actions for an agent and a human to collaboratively and jointly achieve the tasks anticipated by the LLM, and the agent automatically adapts to unexpected changes in human action outcomes and preferences. We evaluate DaTAPlan capabilities in a realistic simulation environment, demonstrating accurate task anticipation, effective human-robot collaboration, and the ability to adapt to unexpected changes. Project website: https://dataplan-hrc.github.io

Nandiraju Gireesh, Ayush Agrawal, Ahana Datta et al.

The Multi-Object Navigation (MultiON) task requires a robot to localize an instance (each) of multiple object classes. It is a fundamental task for an assistive robot in a home or a factory. Existing methods for MultiON have viewed this as a direct extension of Object Navigation (ON), the task of localising an instance of one object class, and are pre-sequenced, i.e., the sequence in which the object classes are to be explored is provided in advance. This is a strong limitation in practical applications characterized by dynamic changes. This paper describes a deep reinforcement learning framework for sequence-agnostic MultiON based on an actor-critic architecture and a suitable reward specification. Our framework leverages past experiences and seeks to reward progress toward individual as well as multiple target object classes. We use photo-realistic scenes from the Gibson benchmark dataset in the AI Habitat 3D simulation environment to experimentally show that our method performs better than a pre-sequenced approach and a state of the art ON method extended to MultiON.

Vishnu Kumar, Saharsh Agarwal, Rama Vadapalli et al.

This paper presents the design of an in-pipe climbing robot that operates using a novel `Three-output open differential'(3-OOD) mechanism to traverse complex networks of pipes. Conventional wheeled/tracked in-pipe climbing robots are prone to slip and drag while traversing in pipe bends. The 3-OOD mechanism helps in achieving the novel result of eliminating slip and drag in the robot tracks during motion. The proposed differential realizes the functional abilities of the traditional two-output differential, which is achieved the first time for a differential with three outputs. The 3-OOD mechanism mechanically modulates the track speeds of the robot based on the forces exerted on each track inside the pipe network, by eliminating the need for any active control. The simulation of the robot traversing in the pipe network in different orientations and in pipe-bends without slip shows the proposed design's effectiveness.

Kartik Suryavanshi, Rama Vadapalli, Praharsha Budharaja et al.

This paper introduces the Omnidirectional Tractable Three Module Robot for traversing inside complex pipe networks. The robot consists of three omnidirectional modules fixed 120° apart circumferentially which can rotate about their axis allowing holonomic motion of the robot. Holonomic motion enables the robot to overcome motion singularity when negotiating T-junctions and further allows the robot to arrive in a preferred orientation while taking turns inside a pipe. The singularity region while negotiating T-junctions is analyzed to formulate the geometry of the region. The design and motion capabilities are validated by conducting simulations in MSC ADAMS on a simplified lumped-model of the robot.

Akash Singh, Vinay Rodrigues, Enna Sachdeva et al.

This paper presents a novel design of a crawler robot which is capable of transforming its chassis from an Omni crawler mode to a large-sized wheel mode using a novel mechanism. The transformation occurs without any additional actuators. Interestingly the robot can transform into a large diameter and small width wheel which enhances its maneuverability like small turning radius and fast/efficient locomotion. This paper contributes on improving the locomotion mode of previously developed hybrid compliant omnicrawler robot CObRaSO. In addition to legged and tracked mechanism, CObRaSO can now display large wheel mode which contributes to its locomotion capabilities. Mechanical design of the robot has been explained in a detailed manner in this paper and also the transforming experiment and torque analysis has been shown clearly

Gautham Vasan, Arun Kumar Singh, Madhava Krishna

This paper presents a method for path-following for quadcopter trajectories in real time. Non-Linear Guidance Logic is used to find the intercepts of the subsequent destination. Trajectory tracking is implemented by formulating the trajectory of the quadcopter using its jerk, in discrete time, and then solving a convex optimization problem on each decoupled axis. Based on the maximum possible thrust and angular rates of the quadcopter, feasibility constraints for the quadcopter have been derived. In this report we describe the design and implementation of explicit MPC controllers where the controllers were executed on a computer using sparse solvers to control the vehicle in hovering flight.