Abstract

Autonomous explorative robots frequently encounter scenarios where multiple future trajectories can be pursued. Often these are cases with multiple paths around an obstacle or trajectory options towards various frontiers. Humans in such situations can inherently perceive and reason about the surrounding environment to identify several possibilities of either manoeuvring around the obstacles or moving towards various frontiers. In this work, we propose a 2 stage Convolutional Neural Network architecture which mimics such an ability to map the perceived surroundings to multiple trajectories that a robot can choose to traverse. The first stage is a Trajectory Proposal Network which suggests diverse regions in the environment which can be occupied in the future. The second stage is a Trajectory Sampling network which provides a finegrained trajectory over the regions proposed by Trajectory Proposal Network. We evaluate our framework in diverse and complicated real life settings. For the outdoor case, we use the KITTI dataset and our own outdoor driving dataset. In the indoor setting, we use an autonomous drone to navigate various scenarios and also a ground robot which can explore the environment using the trajectories proposed by our framework. Our experiments suggest that the framework is able to develop a semantic understanding of the obstacles, open regions and identify diverse trajectories that a robot can traverse. Our comparisons portray the performance gain of the proposed architecture over a diverse set of methods against which it is compared.

Abstract

Planning frameworks for autonomous vehicles must be robust and computationally efficient for real time realization. At the same time, they should accommodate the unpredictable behavior of the other participants and produce safe trajectories. In this paper, we present a computationally efficient hierarchical planning framework for autonomous vehicles that can generate safe trajectories in complex driving scenarios, which are commonly encountered in urban traffic settings. The first level of the proposed framework constructs a Model Predictive Control(MPC) routine using an efficient difference of convex programming approach, that generates smooth and collision-free trajectories. The constraints on curvature and road boundaries are seamlessly integrated into this optimization routine. The second layer is mainly responsible to handle the unpredictable behaviors that are typically exhibited by the other participants of traffic. It is built along the lines of time scaled collision cone(TSCC) which optimize for the velocities along the trajectory to handle such disturbances. We additionally show that our framework maintains optimal balance between temporal and path deviations while executing safe trajectories. To demonstrate the efficacy of the presented framework we validated it in extensive simulations in different driving scenarios like over taking, lane merging and jaywalking among many dynamic and static obstacles.

Abstract

This paper proposes an SVM Enhanced Trajectory Planner for dynamic scenes, typically those encountered in on road settings. Frenet frame based trajectory generation is popular in the context of autonomous driving both in research and industry. We incorporate a safety based maximal margin criteria using a SVM layer that generates control points that are maximally separated from all dynamic obstacles in the scene. A kinematically consistent trajectory generator then computes a path through these waypoints. We showcase through simulations as well as real world experiments on a self driving car that the SVM enhanced planner provides for a larger offset with dynamic obstacles than the regular Frenet frame based trajectory generation. Thereby, the authors argue that such a formulation is inherently suited for navigation amongst pedestrians. We assume the availability of an intent or trajectory prediction module that predicts the future trajectories of all dynamic actors in the scene.

Abstract

Polar codes, introduced by Arikan, achieve the capacity of arbitrary binary-input discrete memoryless channel W under successive cancellation decoding. Any such channel having capacity I(W) and for any coding scheme allowing transmission at rate R, scaling exponent is a parameter which characterizes how fast gap to capacity decreases as a function of code length N for a fixed probability of error. The relation between them is given by N⩾α/(I(W)−R)μ. Scaling exponent for kernels of small size up to L=8 have been exhaustively found. In this paper, we consider product kernels TL obtained by taking Kronecker product of component kernels. We derive the properties of polarizing product kernels relating to number of product kernels, self duality and partial distances in terms of the respective properties of the smaller component kernels. Subsequently, polarization behavior of component kernel Tl is used to calculate scaling exponent of TL=T2⊗Tl. Using this method, we show that μ(T2⊗T5)=3.942. Further, we employ a heuristic approach to construct good kernel of L=14 from kernel having size l=8 having best μ and find μ(T2⊗T7)=3.485.

Abstract

Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with locality. The notion of locality has been extended to hierarchical locality, which allows for locality to gradually increase in levels with the increase in the number of erasures. We consider the locality constraints imposed by codes with two-level hierarchical locality and define maximally recoverable codes with data-local and local hierarchical locality. We derive certain properties related to their punctured codes and minimum distance. We give a procedure to construct hierarchical data-local MRCs from hierarchical local MRCs. We provide a construction of hierarchical local MRCs for all parameters. For the case of one global parity, we provide a different construction of hierarchical local MRC over a lower field size

Abstract

Cooperative regenerating codes are regenerating codes designed to tradeoff storage for repair bandwidth in case of multiple node failures. Minimum storage cooperative regenerating (MSCR) codes are a class of cooperative regenerating codes which achieve the minimum storage point of the tradeoff. Recently, these codes have been constructed for all possible parameters (n, k, d, h), where h erasures are repaired by contacting any d surviving nodes. However, these constructions have very large sub-packetization. ε-MSR codes are a class of codes introduced to tradeoff subpacketization level for a slight increase in the repair bandwidth for the case of single node failures. We introduce the framework of ε-MSCR codes which allow for a similar tradeoff for the case of multiple node failures. We present a construction of ε-MSCR codes, which can recover from two node failures, by concatenating a class of MSCR codes and scalar linear codes. We give a repair procedure to repair the ε-MSCR codes in the event of two node failures and calculate the repair bandwidth for the same. We characterize the increase in repair bandwidth incurred by the method in comparison with the optimal repair bandwidth given by the cut-set bound. Finally, we show the subpacketization level of ε-MSCR codes scales logarithmically in the number of nodes

Abstract

Autonomous explorative robots frequently encounter scenarios where multiple future trajectories can be pursued. Often these are cases with multiple paths around an obstacle or trajectory options towards various frontiers. Humans in such situations can inherently perceive and reason about the surrounding environment to identify several possibilities of either manoeuvring around the obstacles or moving towards various frontiers. In this work, we propose a 2 stage Convolutional Neural Network architecture which mimics such an ability to map the perceived surroundings to multiple trajectories that a robot can choose to traverse. The first stage is a Trajectory Proposal Network which suggests diverse regions in the environment which can be occupied in the future. The second stage is a Trajectory Sampling network which provides a finegrained trajectory over the regions proposed by Trajectory Proposal Network. We evaluate our framework in diverse and complicated real life settings. For the outdoor case, we use the KITTI dataset and our own outdoor driving dataset. In the indoor setting, we use an autonomous drone to navigate various scenarios and also a ground robot which can explore the environment using the trajectories proposed by our framework. Our experiments suggest that the framework is able to develop a semantic understanding of the obstacles, open regions and identify diverse trajectories that a robot can traverse. Our comparisons portray the performance gain of the proposed architecture over a diverse set of methods against which it is compared.

Abstract

Circular perfect graphs are those undirected graphs such that the circular clique number is equal to the circular chromatic number for each induced subgraph. They form a strict superclass of the perfect graphs, whose index coding broadcast rates are well known. We present the broadcast rate of index coding for side-information graphs whose complements are circular perfect, along with an optimal achievable scheme. We thus enlarge the known classes of graphs for which the broadcast rate is exactly characterized. In an attempt to understand the broadcast rate of a graph given that of its complement, we obtain upper and lower bounds for the product and sum of the vector linear broadcast rates of a graph and its complement. We show that these bounds are satisfied with equality even for some perfect graphs. Curating prior results, we show that there are circular perfect but imperfect graphs which satisfy the lower bound on the product of the broadcast rate of the complementary graphs with equality.

Abstract

Coded caching was introduced as a technique of systematically exploiting locally available storage at the clients to increase the channel throughput via coded transmissions. Most known coded caching schemes in literature enable large gains in terms of the rate, however at the cost of subpacketization that is exponential in ( being the number of clients, some positive integer). Building upon recent prior work for coded caching design via line graphs and finite-field projective geometries, we present a new scheme in this work which achieves a subexponential (in ) subpacketization of and rate , for large , and the cached fraction being upper bounded by a constant (for some prime power and constant ). Apart from this asymptotic improvement, we show that through some numerical comparisons that our present scheme has much lower subpacketization than previous comparable …

Abstract

In this paper, we present IVO: Inverse Velocity Obstacles an egocentric framework that improves the real time implementation. The proposed method stems from the concept of velocity obstacle and can be applied for both single agent and multi-agent system. It focuses on computing collision free maneuvers without any knowledge or assumption on the pose and the velocity of the robot. This is primarily achieved by reformulating the velocity obstacle to adapt to an ego-centric framework. This is a significant step towards improving real time implementations of collision avoidance in dynamic environments as there is no dependency on state estimation techniques to infer the robot pose and velocity. We evaluate IVO for both single agent and multi-agent in different scenarios and show it’s efficacy over the existing formulations. We also show the real time scalability of the proposed methodology.