Abstract

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.

Abstract

In this paper we present a non-linear time scaling based formulation for computing time optimal motions along specified paths. The primary motivation behind the current work is to introduce acceleration continuity constraints within the time optimal framework. Such constraint necessitates the use of time varying controls instead of commonly used piecewise constant controls. We propose a novel extension of our previously developed concept of non-linear time scaling through which it is possible to parametrize controls as piece-wise product of a exponential and a linear function. We show that such representation leads to a very simple optimization structure with primarily linear constraints. The non-linearity has a quasi-convex structure which we reformulate into a simple difference of convex form. A sequential convex programming framework is utilised to solve the optimization as a sequence of sparse quadratic programmes. The proposed optimization is an improvement over the current state of the art frameworks which introduces acceleration continuity constraints in the time optimal framework through highly non-linear and non-convex optimizations.

Abstract

Image based reconstruction of urban environments is a challenging problem that deals with optimization of large number of variables, and has several sources of errors like the presence of dynamic objects. Since most large scale approaches make the assumption of observing static scenes, dynamic objects are relegated to the noise modelling section of such systems. This is an approach of convenience since the RANSAC based framework used to compute most multiview geometric quantities for static scenes naturally confine dynamic objects to the class of outlier measurements. However, reconstructing dynamic objects along with the static environment helps us get a complete picture of an urban environment. Such understanding can then be used for important robotic tasks like path planning for autonomous navigation, obstacle tracking and avoidance, and other areas. In this paper, we propose a system for robust SLAM that works in both static and dynamic environments. To overcome the challenge of dynamic objects in the scene, we propose a new model to incorporate semantic constraints into the reconstruction algorithm. While some of these constraints are based on multi-layered dense CRFs trained over appearance as well as motion cues, other proposed constraints can be expressed as additional terms in the bundle adjustment optimization process that does iterative refinement of 3D structure and camera / object motion trajectories. We show results on the challenging KITTI urban dataset for accuracy of motion segmentation and reconstruction of the trajectory and shape of moving objects relative to ground truth. We are able to show average relative error reduction by 41 % for moving object trajectory reconstruction relative to state-of-the-art methods like TriTrack[16], as well as on standard bundle adjustment algorithms with motion segmentation.

Abstract

We propose a novel collision avoidance formulation in the intent space, suitable for navigation of non-holonomic robots in human centered environments. The intent space is characterized by various bands of trajectories wherein each band can be thought to be a representation of a possible human intended motion and the uncertainty associated with it. We ascribe probabilities to human intentions and characterize the uncertainty around it through Gaussian state transition and its concomitant Gaussian parametric distribution. Given an intent space we design avoidance maneuvers based on our recent works on time scaled collision cone concept which provides analytical characterization of collision free velocities in dynamic environments. In this paper, we present a probabilistic variant of the time scaled collision cone which allows us to relate space of collision free velocities to an associated confidence measure. We also develop an optimization framework which extract such specific solutions from the entire solution space that achieves an elegant balance between the objective of minimizing risk and ease of avoidance maneuver. We further show that by accounting for possible intents in human motion, the method transcends the realm of reactive avoidance to proactive anticipation of collisions and its effective avoidance, thereby increasing the overall safety of navigation.

Abstract

Traditional visual servoing is able to navigate a robotic system between two views of the same object. However, it is not designed to servo between views of different objects. In this paper, we consider a novel problem of servoing any instance (exemplar) of an object category to a desired pose (view) and propose a strategy to accomplish the task. We use features that semantically encode the locations of object parts and define the servoing error as the difference between positions of corresponding parts in the image space. Our controller is based on the linear combination of 3D models, such that the resulting model interpolates between the given and desired instances. We conducted our experiments on five different object categories in simulation framework and show that our approach achieves the desired pose with smooth trajectory. Furthermore, we show the performance gain achieved by using a linear …

Abstract

A novel compliant robot is proposed for traversing on unstructured terrains. The robot consists of modules, each containing a link and an active wheel-pair, and neighboring modules are connected using a passive joint. This type of robots are lighter and provide high durability due to the absence of link-actuators. However, they have limited climbing ability due to tendency of tipping over while climbing big obstacles. To overcome this disadvantage, the use of compliant joints is proposed in this work. Stiffness of each compliant joint is estimated by formulating an optimization problem with an objective to minimize link joint moments while maintaining static-equilibrium. This is one of the key novelties of the proposed work. A design methodology is also proposed for developing an n-module compliant robot for climbing a given height on a known surface. The efficacy of the proposed formulation is illustrated using numerical simulations of the three and five module robots. The robot is successfully able to climb maximum heights upto three times and six times the wheel diameter using three and five modules, respectively. A working prototype was developed and the simulation results were successfully validated on it.

Abstract

This paper presents a novel visual servoing controller for a satellite mounted dual-arm space robot. The controller is designed to complete the task of servoing the robot's endeffectors to the desired pose, while regulating orientation of the base-satellite. Task redundancy approach is utilized to coordinate the servoing process and attitude of the base satellite. The visual task is defined as a primary task, while regulating attitude of the base satellite to zero is defined as a secondary task. The secondary task is formulated as an optimization problem in such a way that it does not affect the primary task, and simultaneously minimizes its cost function. A set of numerical experiments are carried out on a dual-arm space robot showing efficacy of the proposed control methodology.

Abstract

Small obstacles of the order of 0.5-3cms and homogeneous scenes often pose a problem for indoor mobile robots. These obstacles cannot be clearly distinguished even with the state of the art depth sensors or laser range finders using existing vision based algorithms. With the advent of sophisticated image processing algorithms like SLIC [1] and LSD [9], it is possible to extract rich information from an image which led us to develop a novel architecture to detect very small obstacles on the floor using a monocular camera. This information is further processed using a Markov Random Field based graph cut formalism that precisely segments the floor and detects obstacles which are extremely low. We show robust and accurate obstacle detection and floor segmentation in diverse environments over a large variety of objects found indoors. In our case, low lying obstacles, changing floor patterns and extremely homogeneous environments are properly classified which leads to a drastic decrease in the number of obstacles that may not be classified by existing robotic vision algorithms.

Abstract

In this paper, we present a posture control scheme for step climbing by an in-house developed three-segmented tracked robot, miniUGV. The posture control scheme results in minimum torque at the actuated joints of the segments. Non-linear optimization is carried out offline for progressively decreasing distance of the robot from the step with torque minimization as objective function and force balance, motor torque limits, slippage avoidance and interference avoidance constraints. The resulting angles of the joints are fitted to a third degree polynomial as a function of the robot distance from the step and the step height. It is shown that a single set of polynomial functions is sufficient for climbing steps of all permissible heights and angles of attack of the front segment. The methodology has been verified through simulation followed by implementation on the real robot. As a consequence of this optimization we find that the average current reduced by more than thirty percent, reducing power consumption and confirming the efficacy of the optimization framework

Abstract

In the field of active perception, object search is a widely studied problem. To search for an object in large rooms, it would be expensive to explore and check each object's similarity with the object of interest. The expense could uncontrollably bloat as the number of objects to be searched increases. If the objects are of the order of a 2-5cm, they appear very small, making it difficult for the present algorithms to recognize them. A general human strategy in such cases is to sparsely identify, from far away (4-6m), if the object of interest is present in the scene. Subsequently, each of the possible objects is analysed from closer proximity to recognize, for further manipulation. In this work, we present a similar framework. We reduce search-space, by identifying existential probability of a small object from a distance followed by a closer 3-D analysis of its point cloud to accurately recognize it. This is achieved by 2-D modelling of the objects using Gaussian Mixture Models followed by recognizing objects using efficient RGB-Depth based algorithm.