Ignacy Duleba

Circular Object Detection Using a Modified Hough Transform

Circular Object Detection Using a Modified Hough Transform A practical modification of the Hough transform is proposed that improves the detection of low-contrast circular objects. The original circular Hough transform and its numerous modifications are discussed and compared in order to improve both the efficiency and computational complexity of the algorithm. Medical images are selected to verify the algorithm. In particular, the algorithm is applied to localize cell nuclei of cytological smears visualized using a phase contrast microscope.

Nonholonomic motion planning based on Newton algorithm with energy optimization

Discusses a modification of the Newton algorithm applied to nonholonomic motion planning with energy optimization. The energy optimization is performed either by optimizing motion in the null space of the Jacobian matrix derived from the nonholonomic system or coupling this motion with movement toward the goal. Resulting controls are smooth and easily generated by motors or thrusters. The two methods can be used, when kinematics are considered, to steer any driftless nonholonomic systems particular free-floating objects, underactuated manipulators, mobile robots (with trailers). Similarities and differences are also discussed in the Newton algorithm for holonomic and nonholonomic systems.

3D Local Trajectory Planner for UAV

In this paper a local trajectory planner is described and applied. This planner works in three dimensional environment populated with static and passive movable obstacles. The main contribution of this paper is a proposal of a new method of autonomous navigation. Novelty of this approach relies on splitting the motion planning problem into two stages: a decision mode and a trace mode. In the decision mode, vehicle selects its current direction of motion on the basis of the current value of a performance index. In the trace mode vehicle traces boundary and edges of obstacles using its on-board sensors. Depending on vehicles environment, the two modes follow one another many times. Another new idea is a negative velocity feedback. The feedback stabilizes velocity of the vehicle around a value considered safe in a given environment. The planner, although autonomous, may be adjusted by higher order system (strategic behavior) by changing its parameters. It is not computationally intensive and therefore can be used in real-time applications.

On inverting singular kinematics and geodesic trajectory generation for robot manipulators

In this paper, a new method is proposed of solving the inverse kinematic problem for robot manipulators whose kinematics are allowed to possess singularities. The method is based upon the so-called generalized Newton algorithm, introduced by S. Smale, and can be adopted to both nonredundant and redundant kinematics. Moreover, given a pair of points in the external space of a manipulator, the method is capable of generating a minimum-length trajectory joining the points (a geodesic), in particular a straight-line trajectory. Results of representative computer experiments, including those with the PUMA 560 kinematics, are reported in order to illustrate the performance of the method.

Modeling and Control of Mobile Manipulators

Abstract In this paper equations of dynamics of a mobile manipulator (Le. a manipulator placed on a mobile platform) are derived. It has been shown that the equations do not display structural properties valid for its manipulator and its mobile platform when considered alone. Required modifications of existing algorithms for controlling manipulators and mobile platforms are highlit to adapt them to steering mobile manipulators. For typical mobile platforms, it has been proven that a motion along straight line segments on the x — y plane is dynamically simpler than any other motion.

On a computationally simple form of the generalized Campbell-Baker-Hausdorff-Dynkin formula

Abstract In this paper a computationally simple form of the generalized Campbell–Baker–Hausdorff–Dynkin formula (GCBHD) is given. Simplifications arise from both combinatorial (explicit) as well as algorithmic (implicit) arguments. On generating the Ph. Hall basis in a special form, and introducing a specific structure representation of the vector field, vector fields appearing in GCBHD are automatically transformed into the reduced Ph. Hall basis. The formula can be exploited in nonholonomic motion planning what is illustrated with examples.

Definition of a kinematic metric for robot manipulators

Using a Riemannian metric in the special Euclidean group we define a kinematic metric on the space of kinematics of robot manipulators. Prospective applications of the metric in kinematic design and performance evaluation of robot manipulators are indicated. For exemplary kinematics, including the PUMA 600, explicit formulas are provided describing the dependence of the metric on manipulators geometric parameters.

Modified Jacobian method of transversal passing through the smallest deficiency singularities for robot manipulators

This paper proposes a method for transversal passing through singularities of corank 1, both for nonredundant and redundant robotic manipulators. The method modifies the Jacobian matrix of manipulators forward kinematics to retrieve its full rank at singularities. Natural candidates for the Jacobian matrix modification are derivatives of determinants of full size sub-matrices of the Jacobian matrix. The method is illustrated with examples, including a PUMA manipulator and 2-link and 3-link planar manipulators. Some restrictions on the applicability of the method for nonredundant manipulators are also discussed.

Velocity space approach to motion planning of nonholonomic systems

In this paper, a velocity space method of motion planning for nonholonomic systems is presented. This method, based on Lie algebraic principles and locally around consecutive current states, plans a motion towards a goal. It is effective as most of the computations can be carried out analytically. This method is illustrated on the unicycle robot and the inverted pendulum.

Layer, Lie algebraic method of motion planning for nonholonomic systems

Abstract In this paper a layer, Lie algebraic method of motion planning for nonholonomic systems is presented. It plans locally a motion towards a goal by searching for optimal directions in equi-cost spaces. The spaces are easy to determine via exploiting Lie algebraic properties of vector fields that define the controlled system. The method was illustrated on the unicycle robot and the inverted pendulum.