Kamal K. Gupta

Fast collision avoidance for manipulator arms: a sequential search strategy

A sequential strategy is presented for planning collision-free motions for a manipulator arm. The basic idea behind the approach is to plan the motion of each link successively, starting from the base link. Suppose that the motion of links to link i (including link i) has been planned. This already determines the path of one end (the proximal end) of link i+1. The motion of link i+1 is now planned along this path by controlling the degree of freedom associated with it, which is a 2-D motion planning problem. This strategy results in one 1-D (the first link is degenerate) and (n-1) 2-D planning problems. The 2-D motion planning problem is to plan the motion of a single link as one end of this link moves along a fixed path. This problem is posed in t* theta space, where t is the parameter along the path and theta the angle to be planned. The obstacles in t* theta space are approximated by discretizing t. Fast and efficient techniques are then used to plan a path in t* theta space. Thus, the strategy leads to fast and efficient algorithms and is especially suited for highly redundant arms. >

The kinematic roadmap: a motion planning based global approach for inverse kinematics of redundant robots

This paper proposes a novel and global approach to solving the point-to-point inverse kinematics problem for highly redundant manipulators. Given an initial configuration of the robot, the problem is to find a reachable configuration that corresponds to a desired position and orientation of the end-effector. Central to our approach is the novel notion of kinematic roadmap for a manipulator. The kinematic roadmap captures the connectivity of the connected component of the free configuration space of the manipulator in a finite graph like structure. The point-to-point inverse kinematics problem is then solved using this roadmap. We provide completeness results for our algorithm. Our implementation of SEARCH is an efficient closed form solution, albeit local, to inverse kinematics that exploits the serial kinematic structure of serial manipulator arms. Initial experiments with a 7-DOF manipulator have been extremely successful.

Motion prediction of moving objects based on autoregressive model

In this paper, we describe a framework for predicting future positions and orientation of moving obstacles in a time-varying environment using autoregressive model (ARM) with conditional maximum likelihood estimate of the model parameters. No constraints are placed on the obstacles motion. The proposed algorithm can be used in a variety of applications, one of which is robot motion planning in time varying environments.

Path planning with general end-effector constraints

In this paper, we address the path planning problem with general end-effector constraints (PPGEC) for robot manipulators. Two approaches are proposed. The first approach is the Adapted-RGD method, which is adapted from an existing randomized gradient descent (RGD) method for closed-chain robots. The second approach is radically different. We call it ATACE, Alternate Task-space And Configuration-space Exploration. Unlike the first approach which searches purely in C-space, ATACE works in both task space and C-space. It explores the task space for end-effector paths satisfying given constraints, and utilizes trajectory tracking technique(s) as a local planner(s) to track these paths in the configuration space. We have implemented both approaches and compared their relative performances in different scenarios. ATACE outperforms Adapted-RGD in the majority (but not all) of the scenarios. We outline intuitive explanations for the relative performances of these two approaches.

Manipulation planning for redundant robots: A practical approach

An emerging paradigm in solving the classical motion- planning problem (among static obstacles) is to capture the connectivity of the configuration space using a finite (but pos sibly large) set of landmarks (or nodes) in it. In this paper, we extend this paradigm to manipulation-planning problem, where the goal is to plan the motion of a robot so that it can move a given object from an initial configuration to a final configuration while avoiding collisions with the static obstacles and other movable objects in the environment. Our specific approach adapts Adriadnes clew algorithm, which has been shown effective for classical motion-planning prob lems (Mazer et al. 1994; Ahuactzin 1994). In our approach, landmarks are placed in lower dimensional submanifolds of the composite configuration space. These landmarks repre sent stable grasps that are reachable from the initial con figuration. From each new landmark, the planner attempts to reach the goal configuration by executing a local plan ner, again in a lower (but different) dimensional submani fold of the composite configuration space. The approach is probabilistically resolution complete, does not assume that a closed-form inverse-kinematics solution for the manipulator is available, and is particularly suitable for redundant manip ulators. We also demonstrate that our approach is practical for realistic problems in three-dimensional environments with manipulator arms having fairly large numbers of degrees of freedom. We have experimented with this approach for a 7- DOF manipulator in 3-D environments with one movable ob ject, and computation times range between a few minutes and a few tens of minutes-in our experiments, between 3 min to 15 min, depending on the task difficulty.

Octree-based hierarchical distance maps for collision detection

In this paper, we propose a novel hierarchical representation for discretized distance maps commonly used in robotics for path planning and collision detection applications. We augment the well-known octree structure for representing distance maps in a hierarchical manner. Our augmented octree based representation drastically reduces the expensive memory requirement compared to voxel-based distance maps while providing substantially better collision-detection performance than by using unaugmented octrees. Although our main motivation has been collision detection in robotics, similar octree distance maps will have wide applications in many other areas including machine vision, computer graphics and so on.

Planning quasi-static fingertip manipulations for reconfiguring objects

We address the global motion planning aspects of dexterous manipulation by a multifingered robotic hand. The specific task we address is: starting from a given initial grasp of a three-dimensional (3-D) object O, find feasible quasistatic trajectories (rolling/sliding motions and forces) for the fingertips to move O to a desired final configuration. We call this the reconfiguration problem. Our planner is based on a two-level algorithm combining a graph search on the configuration space of the object and a local planner that solves for instantaneous quasistatic motions of the entire manipulation system. The planner is used for simulating several complex reconfiguration tasks for smooth objects demonstrating the promise of our approach.

Path planning with general end-effector constraints: using task space to guide configuration space search

In this paper, we address the path planning problem with general end-effector constraints (PPGEC) for robot manipulators. Two approaches are proposed. The first approach is adapted from an existing randomized gradient descent (RGD) method for closed-chain robots. The second approach is radically different. We call it ATACE alternate task-space and configuration-space exploration. Unlike the first approach which searches purely in C-space, ATACE works in both task space and C-space. It explores the task space for end-effector paths satisfying given constraints, and utilizes trajectory tracking technique(s) as a local planner(s) to track these paths in the configuration space. We have implemented both approaches and compare their relative performances in different scenarios. ATACE outperforms RGD in majority (but not all) of the scenarios. We outline intuitive explanations for the relative performances of these two approaches.

C-space Entropy: A Measure for View Planning and Exploration for General Robot-Sensor Systems in Unknown Environments

We consider the view planning problem where a range sensor is mounted on a robot mechanism with non-trivial geometry and kinematics. The robot-sensor system is required to explore the environment for obstacles and free space. We present an information theoretical approach in which the sensing action is viewed as reducing ignorance of the planning space, the C-space of the robot. The concept of C-space entropy is introduced as a measure of this ignorance. The next view in the planning process is so chosen that it maximizes the expected reduction of C-space entropy, called the maximal (expected) entropy reduction (MER) criterion. We derive closed-form expressions for expected entropy reduction for an idealized point field-of-view sensor under a Poisson point process model of the environment. We show via simulations and real experiments that the MER criterion is significantly more efficient in sensor-based path planning and exploration tasks than other purely physical space based criteria previously used in the literature.

Global path planning for robust Visual Servoing in complex environments

We incorporate sampling-based global path planning with Visual Servoing (VS) for a robotic arm equipped with an in-hand camera. The path planning accounts for a number of constraints: 1) maintaining continuous visibility of the target within the cameras field of view, 2) avoiding visual occlusion of target features caused by the workspace obstacles, robots body, or the target itself, 3) avoiding collision with physical obstacles or self collision, and 4) joint limits. Incorporating these constraints enhances the applicability of VS to significantly more complex environments/tasks, thereby making the resulting VS much more robust. The proposed planner explores the camera space, i.e. 3D Cartesian space, for permissible camera paths satisfying the aforementioned constraints by iteratively extending a search tree in camera space and simultaneously tracking these paths in the robots joint space using a local planner. The planned camera path is then projected into the image space and tracked using an image-based visual servoing scheme. The validity and effectiveness of the proposed approach in accomplishing VS tasks in complex environments are demonstrated through a number of simulations on a 6-dof robot arm moving among obstacles.