Centralized trajectory optimization in the joint space of multiple robots allows access to a larger feasible space that can result in smoother trajectories, especially while planning in tight spaces. Unfortunately, it is often computationally intractable beyond a very small swarm size. In this paper, we propose Flow-Opt, a fast learning-based approach for providing high-quality approximations of centralized multi-robot trajectory optimization. Specifically, we reduce the problem to first learning a generative model to sample different candidate trajectories and then using a learned Safety-Filter(SF) to ensure fast inference-time constraint satisfaction. We propose a flow-matching model based on a diffusion transformer (DiT) augmented with state and map encoders, as the generative model. We develop a custom solver for our SF and equip it with a neural network that predicts context-specific initialization. The initialization network is trained in a self-supervised manner, taking advantage of the differentiability of the SF solver. We advance the state-of-the-art in the following respects. First, we show that we can generate trajectories for tens of robots in cluttered environments in a few tens of milliseconds. This is several times faster than existing centralized optimization approaches. Moreover, our approach generates smoother trajectories orders of magnitude faster than competing baselines based on diffusion models. Second, each component of our approach can be batched, allowing us to solve a few tens of problem instances in a fraction of a second. We believe this is the first such result; no existing approach provides such capabilities. Finally, our approach can generate a diverse set of trajectories between a given set of start and goal locations, which can capture different collision-avoidance behaviors.

Dual-arm manipulation is an area of growing interest in the robotics community. Enabling robots to perform tasks that require the coordinated use of two arms, is essential for complex manipulation tasks such as handling large objects, assembling components, and performing human-like interactions. However, achieving effective dual-arm manipulation is challenging due to the need for precise coordination, dynamic adaptability, and the ability to manage interaction forces between the arms and the objects being manipulated. We propose a novel pipeline that combines the advantages of policy learning based on environment feedback and gradient-based optimization to learn controller gains required for the control outputs. This allows the robotic system to dynamically modulate its impedance in response to task demands, ensuring stability and dexterity in dual-arm operations. We evaluate our pipeline on a trajectory-tracking task involving a variety of large, complex objects with different masses and geometries. The performance is then compared to three other established methods for controlling dual-arm robots, demonstrating superior results. Project page: https://dualarmvil.github.io/Dual-Arm-VIL/

Navigation amongst densely packed crowds remains a challenge for mobile robots. The complexity increases further if the environment layout changes, making the prior computed global plan infeasible. In this paper, we show that it is possible to dramatically enhance crowd navigation by just improving the local planner. Our approach combines generative modelling with inference-time optimization to generate sophisticated long-horizon local plans at interactive rates. More specifically, we train a Vector Quantized Variational AutoEncoder to learn a prior over the expert trajectory distribution conditioned on the perception input. At run-time, this is used as an initialization for a sampling-based optimizer for further refinement. Our approach does not require any sophisticated prediction of dynamic obstacles and yet provides state-of-theart performance. In particular, we compare against the recent DRL-VO approach [2] and show a 40% improvement in success rate and a 6% improvement in travel time.

Drivable Free-space prediction is a fundamental and crucial problem in autonomous driving. Recent works have addressed the problem by representing the entire non-obstacle road regions as the free-space. In contrast our aim is to estimate the driving corridors that are a navigable subset of the entire road region. Unfortunately, existing corridor estimation methods directly assume a BEV-centric representation, which is hard to obtain. In contrast, we frame drivable free-space corridor prediction as a pure image perception task, using only monocular camera input. However such a formulation poses several challenges as one doesn’t have the corresponding data for such free-space corridor segments in the image. Consequently, we develop a novel self-supervised approach for free-space sample generation by leveraging future ego trajectories and front-view camera images, making the process of visual corridor estimation dependent on the ego trajectory. We then employ a diffusion process to model the distribution of such segments in the image. However, the existing binary mask-based representation for a segment poses many limitations. Therefore, we introduce ContourDiff, a specialized diffusion-based architecture that denoises over contour points rather than relying on binary mask representations, enabling structured and interpretable free-space predictions. We evaluate our approach qualitatively and quantitatively on both nuScenes and CARLA, demonstrating its effectiveness in accurately predicting safe multimodal navigable corridors in the image.

Quadrotor motion planning in complex environments leverage the concept of safe flight corridor (SFC) to facilitate static obstacle avoidance. Typically, SFCs are constructed through convex decomposition of the environment’s free space into cuboids, convex polyhedra, or spheres. However, such SFCs can be overly conservative when dealing with a quadrotor swarm, substantially limiting the available free space for quadrotors to coordinate. This paper presents an Alternating Minimization-based approach that does not require building a conservative free-space approximation. Instead, both static and dynamic collision constraints are treated in a unified manner. Dynamic collisions are handled based on shared position trajectories of the quadrotors. Static obstacle avoidance is coupled with distance queries from the Octomap, providing an implicit non-convex decomposition of free space. As a result, our approach is scalable to arbitrary complex environments. Through extensive comparisons in simulation, we demonstrate a 60% improvement in success rate, an average 1.8× reduction in mission completion time, and an average 23× reduction in per-agent computation time compared to SFC-based approaches. We also experimentally validated our approach using a Crazyflie quadrotor swarm of up to 12 quadrotors in obstacle-rich environments. The code, supplementary materials, and videos are released for reference.

This work introduces Talk2BEV, a large vision-language model (LVLM)1interface for bird’s-eye view (BEV) maps commonly used in autonomous driving. While existing perception systems for autonomous driving scenarios have largely focused on a pre-defined (closed) set of object categories and driving scenarios, Talk2BEV eliminates the need for BEV-specific training, relying instead on well-performing pre-trained LVLMs. This enables a single system to cater to a variety of autonomous driving tasks encompassing visual and spatial reasoning, predicting the intents of traffic actors, and decision-making based on visual cues. We extensively evaluate Talk2BEV on a large number of scene understanding tasks that rely on both the ability to interpret freeform natural language queries, and in grounding these queries to the visual context embedded into the language-enhanced BEV map. To enable further research in LVLMs for autonomous driving scenarios, we develop and release Talk2BEV-Bench, a benchmark encompassing 1000 human-annotated BEV scenarios, with more than 20,000 questions and ground-truth responses from the NuScenes dataset. We encourage the reader to view the demos on our project page: https://llmbev.github.io/talk2bev/

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 within a certain time limit. 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.

Sampling trajectories from a distribution followed by ranking them based on a specified cost function is a common approach in autonomous driving. Typically, the sampling distribution is hand-crafted (e.g a Gaussian, or a grid). Recently, there have been efforts towards learning the sampling distribution through generative models such as Conditional Variational Autoencoder (CVAE). However, these approaches fail to capture the multi-modality of the driving behaviour due to the Gaussian latent prior of the CVAE. Thus, in this paper, we re-imagine the distribution learning through vector quantized variational autoencoder (VQ-VAE), whose discrete latent-space is well equipped to capture multi-modal sampling distribution. The VQ-VAE is trained with demonstration data of optimal trajectories. We further propose a differentiable optimization based safety filter to minimally correct the VQ-VAE sampled trajectories to ensure collision avoidance. We use backpropagation through the optimization layers in a self-supervised learning set-up to learn good initialization and optimal parameters of the safety filter. We perform extensive comparisons with state-of-the-art CVAE-based baseline in dense and aggressive traffic scenarios and show a reduction of up to 12 times in collision-rate while being competitive in driving speeds.

Navigation of wheeled vehicles on uneven terrain necessitates going beyond the 2D approaches for trajectory planning. Specifically, it is essential to incorporate the full 6dof variation of vehicle pose and its associated stability cost in the planning process. To this end, most recent works aim to learn a neural network model to predict vehicle evolution. However, such approaches are data-intensive and fraught with generalization issues.In this paper, we present a purely model-based approach that just requires the digital elevation information of the terrain. Specifically, we express the wheel-terrain interaction and 6dof pose prediction as a non-linear least squares (NLS) problem. As a result, trajectory planning can be viewed as a bi-level optimization. The inner optimization layer predicts the pose on the terrain along a given trajectory, while the outer layer deforms the trajectory itself to reduce the stability and kinematic costs of the pose.We improve the state-of-the-art in the following respects. First, we show that our NLS-based pose prediction closely matches the output of a high-fidelity physics engine. This result, coupled with the fact that we can query gradients of the NLS solver, makes our pose predictor a differentiable wheel-terrain interaction model. We further leverage this differentiability to efficiently solve the proposed bi-level trajectory optimization problem. Finally, we perform extensive experiments and comparisons with a baseline to showcase the effectiveness of our approach in obtaining smooth, stable trajectories.

Existing Vision-Language Models (VLMs) produce long-term trajectory waypoints or directly control actions based on their perception input and language prompt. However, these VLMs are not explicitly aware of the constraints imposed by the scene or kinematics of the vehicle. As a result, the generated trajectories or control inputs are likely to be unsafe and/or infeasible. In this paper, we introduce LeGo-Drive†, which aims to address these issues. Our key idea is to use the VLM to just predict a goal location based on the given language command and perception input, which is then fed to a downstream differentiable trajectory optimizer with learnable components. We train the VLM and the trajectory optimizer in an end-to-end fashion using a loss function that captures the ego-vehicle’s ability to reach the predicted goal while satisfying safety and kinematic constraints. The gradients during the back-propagation flow through the optimization layer and make the VLM aware of the planner’s capabilities, making more feasible goal predictions. We compare our end-to-end approach with a decoupled framework where the planner is just used at the inference time to drive to the VLM-predicted goal location and report a goal reaching Success Rate of 81%. We demonstrate the versatility of LeGo-Drive†across various driving scenarios and navigation commands, highlighting its potential for practical deployment in autonomous vehicles.

This paper presents a scalable online algorithm to generate safe and kinematically feasible trajectories for quadrotor swarms. Existing approaches rely on linearizing Euclidean distance-based collision constraints and on axis-wise decoupling of kinematic constraints to reduce the trajectory optimization problem for each quadrotor to a quadratic program (QP). This conservative approximation often fails to find a solution in cluttered environments. We present a novel alternative that handles collision constraints without linearization and kinematic constraints in their quadratic form while still retaining the QP form. We achieve this by reformulating the constraints in a polar form and applying an Alternating Minimization algorithm to the resulting problem. Through extensive simulation results, we demonstrate that, as compared to Sequential Convex Programming (SCP) baselines, our approach achieves on average, a 72% improvement in success rate, a 36% reduction in mission time, and a 42 times faster per-agent computation time. We also show that collision constraints derived from discrete-time barrier functions (BF) can be incorporated, leading to different safety behaviours without significant computational overhead. Moreover, our optimizer outperforms the state-of-the-art optimal control solver ACADO in handling BF constraints with a 31 times faster per-agent computation time and a 44% reduction in mission time on average. We experimentally validated our approach on a Crazyflie quadrotor swarm of up to 12 quadrotors. The code with supplementary material and video are released for reference.

This paper presents a real-time algorithm for computing the optimal sequence and motion plans for a fixed-base manipulator to pick and place a set of given objects. The optimality is defined in terms of the total execution time of the sequence or its proxy, the arc-length in the joint-space. The fundamental complexity stems from the fact that the optimality metric depends on the joint motion, but the task specification is in the end-effector space. Moreover, mapping between a pair of end-effector positions to the shortest arc-length joint trajectory is not analytic; instead, it entails solving a complex trajectory optimization problem. Existing works ignore this complex mapping and use the Euclidean distance in the end-effector space to compute the sequence. In this paper, we overcome the reliance on the Euclidean distance heuristic by introducing a novel data-driven technique to estimate the optimal arc-length cost in joint space (a.k.a the value function) between two given end-effector positions. We parametrize the value function as a Neural Network and motivate a niche choice for its architecture, inspired by the works on metric learning. The learned value function is then used as an edge cost in a capacitated vehicle routing problem (CVRP) set-up to compute the optimal visitation sequence. Finally, we optimize over the input space of the learnt value function network to propose a novel Inverse Kinematics (IK) algorithm that produces substantially shorter joint arc-length trajectories than existing approaches while executing the computed optimal sequence. We show that our sequence planner, in combination with our proposed IK, offers a substantial improvement in joint arc-length over existing state-of-the-art while maintaining scalability to a large number of objects.

Safe autonomous driving critically depends on how well the ego-vehicle can predict the trajectories of neighboring vehicles. To this end, several trajectory prediction algorithms have been presented in the existing literature. Many of these approaches output a multimodal distribution of obstacle trajectories instead of a single deterministic prediction to account for the underlying uncertainty. However, existing planners cannot handle the multimodality based on just sample-level information of the predictions. With this motivation, this paper proposes a trajectory optimizer that can leverage the distributional aspects of the prediction in a computationally tractable and sample-efficient manner. Our optimizer can work with arbitrarily complex distributions and thus can be used with output distribution represented as a deep neural network. The core of our approach is built on embedding distribution in Reproducing Kernel Hilbert Space (RKHS), which we leverage in two ways. First, we propose an RKHS embedding approach to select probable samples from the obstacle trajectory distribution. Second, we rephrase chance-constrained optimization as distribution matching in RKHS and propose a novel sampling-based optimizer for its solution. We validate our approach with handcrafted and neural network-based predictors trained on real-world datasets and show improvement over the existing stochastic optimization approaches in safety metrics.

Trajectory sampling in the Frenet(road-aligned) frame, is one of the most popular methods for motion planning of autonomous vehicles. It operates by sampling a set of behavioral inputs, such as lane offset and forward speed, before solving a trajectory optimization problem conditioned on the sampled inputs. The sampling is handcrafted based on simple heuristics, does not adapt to driving scenarios, and is oblivious to the capabilities of downstream trajectory planners. In this paper, we propose an end-to-end learning of behavioral input distribution from expert demonstrations or in a self-supervised manner. We embed a novel differentiable trajectory optimizer as a layer in neural networks, allowing us to update behavioral inputs by considering the optimizer's feedback. Moreover, our end-to-end approach also ensures that the learned behavioral inputs aid the convergence of the optimizer. We improve the state-of-the-art in the following aspects. First, we show that learned behavioral inputs substantially decrease collision rate while improving driving efficiency over handcrafted approaches. Second, our approach outperforms model predictive control methods based on sampling-based optimization.

We present CCO-VOXEL: the very first chance-constrained optimization (CCO) algorithm that can compute trajectory plans with probabilistic safety guarantees in real-time directly on the voxel-grid representation of the world. CCO-VOXEL maps the distribution over the distance to the closest obstacle to a distribution over collision-constraint violation and computes an optimal trajectory that minimizes the violation probability. Importantly, unlike existing works, we never assume the nature of the sensor uncertainty or the probability distribution of the resulting collision-constraint violations. We leverage the notion of Hilbert Space embedding of distributions and Maximum Mean Discrepancy (MMD) to compute a tractable surrogate for the original chance-constrained optimization problem and employ a combination of A* based graph-search and Cross-Entropy Method for obtaining its minimum. We show tangible performance gain in terms of collision avoidance and trajectory smoothness as a consequence of our probabilistic formulation vis a vis state-of-the-art planning methods that do not account for such non-parametric noise. Finally, we also show how a combination of low-dimensional feature embedding and pre-caching of Kernel Matrices of MMD allow us to achieve real-time performance in simulations as well as in implementations on on-board commodity hardware that controls the quadrotor flight.

Modern autonomous vehicles (AVs) often rely on vision, LIDAR, and even radar-based simultaneous localization and mapping (SLAM) frameworks for precise localization and navigation. However, modern SLAM frameworks often lead to unacceptably high levels of drift (i.e., localization error) when AVs observe few visually distinct features or encounter occlusions due to dynamic obstacles. This paper argues that minimizing drift must be a key desiderata in AV motion planning, which requires an AV to take active control decisions to move towards feature-rich regions while also minimizing conventional control cost. To do so, we first introduce a novel data-driven perception module that observes LIDAR point clouds and estimates which features/regions an AV must navigate towards for drift minimization. Then, we introduce an interpretable model predictive controller (MPC) that moves an AV toward such feature-rich regions while avoiding visual occlusions and gracefully trading off drift and control cost. Our experiments on challenging, dynamic scenarios in the state-of-the-art CARLA simulator indicate our method reduces drift up to 76.76% compared to benchmark approaches.

Most commercially available fixed-wing aerial vehicles (FWV) can carry only small, lightweight computing hardware such as Jetson TX2 onboard. Solving non-linear trajectory optimization on these computing resources is computationally challenging even while considering only the kinematic motion model. Most importantly, the computation time increases sharply as the environment becomes more cluttered. In this paper, we take a step towards overcoming this bottleneck and propose a trajectory optimizer that achieves online performance on both conventional laptops/desktops and Jetson TX2 in a typical urban environment setting. Our optimizer builds on the novel insight that the seemingly non-linear trajectory optimization problem for FWV has an implicit multi-convex structure. Our optimizer exploits these computational structures by bringing together diverse concepts from Alternating Minimization, Bregman iteration, and Alternating Direction Method of Multipliers. We show that our optimizer outperforms the state-of-the-art implementation of sequential quadratic programming approach in optimal control solver ACADO in computation time and solution quality measured in terms of control and goal reaching cost.

Autonomous cars and fixed-wing aerial vehicles have the so-called non-holonomic kinematics which non-linearly maps control input to states. As a result, trajectory optimization with such a motion model becomes highly non-linear and non-convex. In this paper, we improve the computational tractability of non-holonomic trajectory optimization by reformulating it in terms of a set of bi-convex cost and constraint functions along with a non-linear penalty. The bi-convex part acts as a relaxation for the non-holonomic trajectory optimization while the residual of the penalty dictates how well its output obeys the non-holonomic behavior. We adopt an alternating minimization approach for solving the reformulated problem and show that it naturally leads to the replacement of the challenging non-linear penalty with a globally valid convex surrogate. Along with the common cost functions modeling goal-reaching, trajectory smoothness, etc., the proposed optimizer can also accommodate a class of non-linear costs for modeling goal-sets, while retaining the bi-convex structure. We benchmark the proposed optimizer against off-the-shelf solvers implementing sequential quadratic programming and interior-point methods and show that it produces solutions with similar or better cost as the former while significantly outperforming the latter. Furthermore, as compared to both off-the-shelf solvers, the proposed optimizer achieves more than 20x reduction in computation time.

Trajectory optimization problems under affine motion model and convex cost function are often solved through the convex-concave procedure (CCP), wherein the non-convex collision avoidance constraints are replaced with its affine approximation. Although mathematically rigorous, CCP has some critical limitations. First, it requires a collision-free initial guess of solution trajectory which is difficult to obtain, especially in dynamic environments. Second, at each iteration, CCP involves solving a convex constrained optimization problem which becomes prohibitive for real-time computation even with a moderate number of obstacles, if long planning horizons are used.In this paper, we propose a novel trajectory optimizer which like CCP involves solving convex optimization problems but can work with an arbitrary initial guess. Moreover, the proposed optimizer can be computationally upto a few orders of magnitude faster than CCP while achieving similar or better optimal cost. The reduced computation time, in turn, stems from some interesting mathematical structures in the optimizer which allows for distributed computation and obtaining solutions in symbolic form. We validate our claims on difficult benchmarks consisting of static and dynamic obstacles.

We present PRVO, a probabilistic variant of Reciprocal Velocity Obstacle (RVO) for decentralized multi-robot navigation under uncertainty. PRVO characterizes the space of velocities that would allow each robot to fulfill its share in collision avoidance with a specified probability. PRVO is modeled as chance constraints over the velocity level constraints defined by RVO and takes into account the uncertainty associated with both state estimation as well as the actuation of each robot. Since chance constraints are in general computationally intractable, we propose a series of reformulations which when combined with time scaling based concepts leads to a closed form characterization of solution space of PRVO for a given probability of collision avoidance. We validate our formulation through numerical simulations in which we highlight the advantages of PRVO over the related existing formulations.

Navigating non-holonomic mobile robots in dynamic environments is challenging because it requires computing at each instant, the space of collision free velocities, characterized by a set of highly non-linear and non-convex inequalities. Moreover, uncertainty in obstacle trajectories further increases the complexity of the problem, as it now becomes imperative to relate the space of collision free velocities to a confidence measure. In this paper, we present a novel perspective towards analyzing and solving probabilistic collision avoidance constraints based on our previous works on non-linear time scaling. In particular, we have shown earlier that a time scaled version of collision cone constraints can be solved in closed form and thus can be used to efficiently characterize the space of collision free velocities. In the current proposed work, we present a probabilistic version of time scaled collision cone constraints obtained by representing obstacle states through generic probability distributions. We present a novel reformulation of the probabilistic constraints into a family of deterministic algebraic constraints. The solution space of each member of the family can be derived in closed form and at the same time, can also be related to the lower bound on confidence measure through Cantelli's inequality. Thus, the proposed work represents a significant improvement over the current state of the art frameworks where probabilistic collision avoidance constraints are solved through exhaustive sampling in the state-control space. We also present a cost metric which serves as the basis for the construction of the various collision avoidance maneuvers based on factors like deviation from the current path, acceleration/de-acceleration capability of the robot, confidence of collision avoidance etc. We very briefly explain how the current robot state can be connected to the solution space of safe velocities in smooth time optimal fashion. Finally, the validity of the proposed formulation is exhibited through extensive numerical simulation results.

Computing time optimal motions along specified paths forms an integral part of the solution methodology for many motion planning problems. Conventionally, this optimal control problem is solved considering piece-wise constant parametrization for the control input which leads to convexity and sparsity in the optimization structure. However, it also results in discontinuous control trajectory which is difficult to track. Thus, in this paper we revisit this time optimal control problem with the primary motivation of ensuring a high degree of smoothness in the resulting motion profile. In particular, we solve it with continuity constraints in control and higher order motion derivatives like jerk, snap etc. It is clear that such constraints would necessitate the use of time varying control inputs over the commonly used piece-wise constant form. The primary contribution of the current work lies in the introduction of a C∞class of time scaling functions represented as parametric exponentials. This in turn allows us to represent time varying control inputs as products of parametric exponential and a polynomial functions. We present the motivation behind adopting such representation of time scaling function over more common polynomial forms, both from mathematical as well as implementation standpoint. We also show that the proposed representation of time scaling function and control input leads to a very simple optimization structure where most of the constraints are linear. The non-linearity has a quasi-convex structure which can be reformulated into a simple difference of convex form. Thus, the resulting optimization can be efficiently solved through sequential convex programming where, at each iteration, the constraints in difference of convex form are further simplified to more conservative linear constraints.

Overtaking of a vehicle moving on structured roads is one of the most frequent driving behavior. In this work, we have described a Real Time Control System based framework for overtaking maneuver of autonomous vehicles. Proposed framework incorporates Intelligent Planning and Modular control modules. Intelligent Planning module of the framework enables the vehicle to intelligently select the most appropriate behavioral characteristics given the perceived operating environment. Subsequently, Modular control module reduces the search space of overtaking trajectories through an SVM based learning approach. These trajectories are then examined for possible future time collision using Velocity Obstacle. It employs non linear time scaling that provides for continuous trajectories in the space of linear and angular velocities to achieve continuous curvature overtaking maneuvers respecting velocity and acceleration bounds. Further time scaling also can scale velocities to avoid collisions and can compute a time optimal trajectory for the learned behavior. The preliminary results show the appropriateness of our proposed framework in virtual urban environment.

The current paper proposes a trajectory optimization approach for navigating a non-holonomic wheeled mobile robot in dynamic environments. The dynamic obstacle's motion is not known and hence is represented by a band of predicted trajectories. The trajectory optimization can account for large number of predicted obstacle trajectories and seeks to avoid each predicted trajectory of every obstacle in the sensing range of the robot. The two primary contributions of the proposed trajectory optimization are (1): A computationally efficient method for computing the intersection space of collision avoidance constraints of large number of predicted obstacle trajectories. (2): A optimization framework to connect the current state to the solution space in time optimal fashion. The intersection/solution space computation is build on our earlier proposed concept of time scaled collision cone, which can be solved in closed form to obtain a set of formulae. These formulae describe how much and in what manner the temporal specification of a trajectory needs to be changed to avoid a given set of dynamic obstacles. This allows us to quickly evaluate solution space of time scaled collision cone over various candidate trajectories, thus reducing the problem of computing the intersection space to that of generating multiple homotopic trajectories. The optimization framework used to connect the current state to the solution space in time optimal fashion is based on the concept of non-linear time scaling, which induces a difference of convex form structure. Thus, on the theoretical side, we show that the various components of the proposed framework are computationally simple and involves solving sets of linear equations and using state of the art convex programming techniques. On the practical side we show that the proposed planner performs better than sampling based planners which treat dynamic obstacles as static over a short duration of time.

In this paper we consider the problem of coordinating the motion of the manipulator and the vehicle to produce stable trajectories for the combined mobile manipulator system on uneven terrain. These kinds of situations often arise in planetary exploration, where rovers equipped with a manipulator are required to navigate over general uneven terrain. Moreover the framework can also be used in situations where the mobile manipulator is required to transport objects on uneven terrain. We generate feasible trajectories for the vehicle between a given start and a goal point considering the dynamics of the manipulator. The framework proposed in the paper plans such motion profile of the manipulator that maximizes vehicle stability which is measured by a novel concept called Feasible Acceleration Count (FAC). We show that, from the point of view of motion planning of mobile manipulator on uneven terrains, FAC gives a better estimate of vehicle stability than more popular metrics like Tip-Over Stability. The trajectory planner closely resembles motion primitive based graph based planning and is combined with a novel cost function derived from FAC. The efficacy of the approach is shown through simulations of a mobile manipulator system on a 2.5D uneven terrain.

In this paper we introduce a novel framework of generating trajectories which explicitly satisfies the stability constraints such as no-slip and permanent ground contact on uneven terrain. The main contributions of this paper are: (1) It derives analytical functions depicting the evolution of the vehicle on uneven terrain. These functional descriptions enable us to have a fast evaluation of possible vehicle stability along various directions on the terrain and this information is used to control the shape of the trajectory. (2) It introduces a novel paradigm wherein non-linear time scaling brought about by parametrized exponential functions are used to modify the velocity and acceleration profile of the vehicle so that these satisfy the no-slip and contact constraints. We show that nonlinear time scaling manipulates velocity and acceleration profile in a versatile manner and consequently has exceptional utility not only in uneven terrain navigation but also in general in any problem where it is required to change the velocity of the robot while keeping the path unchanged like collision avoidance.

In this paper a novel suspension mechanism for rough terrain mobility is proposed. The proposed mechanism is simpler than the existing suspension mechanism in the sense that the number of links and joints has been significantly reduced without compromising the climbing ability of the rover. We explore the use of compliant elements like springs for passively controlling the degree of freedom of the proposed mechanism and a framework for optimizing the spring parameters has been proposed. A performance evaluation of the proposed mechanism has been shown in terms of extensive simulations.