Canonical Subproblems for Robot Inverse Kinematics

The inverse kinematics (IK) problem for many common robot manipulators may be decomposed into canonical subproblems which are solved by finding the angles on circles where they intersect with other geometric objects. We present new algebraic solutions and geometric interpretations for six subproblems using a linear algebra approach, and we demonstrate significant computational performance improvements over existing IK methods. We show that IK for any 6-dof all revolute (6R) robot with three intersecting or parallel joint axes may be solved in closed form using subproblem decomposition. For any other 6R robot, subproblem decomposition reduces finding all IK solutions to a search over one or two joint angles. The first three subproblems, called the Paden-Kahan subproblems, are Subproblem 1: Circle and Point, Subproblem 2: Two Circles, and Subproblem 3: Circle and Sphere. The other three subproblems, which have not been extensively covered in the literature, are Subproblem 4: Circle and Plane, Subproblem 5: Three Circles, and Subproblem 6: Four Circles. Our approach also finds the least-squares solutions for Subproblems 1-4 when the exact solution does not exist.Comment: 14 pages, 8 figures. Updated with new solution methods and timing result

Trajectory Generation for a Multibody Robotic System: Modern Methods Based on Product of Exponentials

This work presents several trajectory generation algorithms for multibody robotic systems based on the Product of Exponentials (PoE) formulation, also known as screw theory. A PoE formulation is first developed to model the kinematics and dynamics of a multibody robotic manipulator (Sawyer Robot) with 7 revolute joints and an end-effector. In the first method, an Inverse Kinematics (IK) algorithm based on the Newton-Raphson iterative method is applied to generate constrained joint-space trajectories corresponding to straight-line and curvilinear motions of the end effector in Cartesian space with finite jerk. The second approach describes Constant Screw Axis (CSA) trajectories which are generated using Machine Learning (ML) and Artificial Neural Networks (ANNs) techniques. The CSA method smooths the trajectory in the Special Euclidean (SE(3)) space. In the third approach, a multi-objective Swarm Intelligence (SI) trajectory generation algorithm is developed, where the IK problem is tackled using a combined SI-PoE ML technique resulting in a joint trajectory that avoids obstacles in the workspace, and satisfies the finite jerk constraint on end-effector while minimizing the torque profiles. The final method is a different approach to solving the IK problem using the Deep Q-Learning (DQN) Reinforcement Learning (RL) algorithm which can generate different joint space trajectories given the Cartesian end-effector path. For all methods above, the Newton-Euler recursive algorithm is implemented to compute the inverse dynamics, which generates the joint torques profiles. The simulated torque profiles are experimentally validated by feeding the generated joint trajectories to the Sawyer robotic arm through the developed Robot Operating System (ROS) - Python environment in the Software Development Kit (SDK) mode. The developed algorithms can be used to generate various trajectories for robotic arms (e.g. spacecraft servicing missions)

Modular and Analytical Methods for Solving Kinematics and Dynamics of Series-Parallel Hybrid Robots

While serial robots are known for their versatility in applications, larger workspace, simpler modeling and control, they have certain disadvantages like limited precision, lower stiffness and poor dynamic characteristics in general. A parallel robot can offer higher stiffness, speed, accuracy and payload capacity, at the downside of a reduced workspace and a more complex geometry that needs careful analysis and control. To bring the best of the two worlds, parallel submechanism modules can be connected in series to achieve a series-parallel hybrid robot with better dynamic characteristics and larger workspace. Such a design philosophy is being used in several robots not only at DFKI (for e.g., Mantis, Charlie, Recupera Exoskeleton, RH5 humanoid etc.) but also around the world, for e.g. Lola (TUM), Valkyrie (NASA), THOR (Virginia Tech.) etc.These robots inherit the complexity of both serial and parallel architectures. Hence, solving their kinematics and dynamics is challenging because they are subjected to additional geometric loop closure constraints. Most approaches in multi-body dynamics adopt numerical resolution of these constraints for the sake of generality but may suffer from inaccuracy and performance issues. They also do not exploit the modularity in robot design. Further, closed loop systems can have variable mobility, different assembly modes and can impose redundant constraints on the equations of motion which deteriorates the quality of many multi-body dynamics solvers. Very often only a local view to the system behavior is possible. Hence, it is interesting for geometers or kinematics researchers, to study the analytical solutions to geometric problems associated with a specific type of parallel mechanism and their importance over numerical solutions is irrefutable. Techniques such as screw theory, computational algebraic geometry, elimination and continuation methods are popular in this domain. But this domain specific knowledge is often underrepresented in the design of model based kinematics and dynamics software frameworks. The contributions of this thesis are two-fold. Firstly, a rigorous and comprehensive kinematic analysis is performed for the novel parallel mechanisms invented recently at DFKI-RIC such as RH5 ankle mechanism and Active Ankle using approaches from computational algebraic geometry and screw theory. Secondly, the general idea of a modular software framework called Hybrid Robot Dynamics (HyRoDyn) is presented which can be used to solve the geometry, kinematics and dynamics of series-parallel hybrid robotic systems with the help of a software database which stores the analytical solutions for parallel submechanism modules in a configurable and unit testable manner. HyRoDyn approach is suitable for both high fidelity simulations and real-time control of complex series-parallel hybrid robots. The results from this thesis has been applied to two robotic systems namely Recupera-Reha exoskeleton and RH5 humanoid. The aim of this software tool is to assist both designers and control engineers in developing complex robotic systems of the future. Efficient kinematic and dynamic modeling can lead to more compliant behavior, better whole body control, walking and manipulating capabilities etc. which are highly desired in the present day and future robotic applications

Path planning for robotic truss assembly

A new Potential Fields approach to the robotic path planning problem is proposed and implemented. Our approach, which is based on one originally proposed by Munger, computes an incremental joint vector based upon attraction to a goal and repulsion from obstacles. By repetitively adding and computing these 'steps', it is hoped (but not guaranteed) that the robot will reach its goal. An attractive force exerted by the goal is found by solving for the the minimum norm solution to the linear Jacobian equation. A repulsive force between obstacles and the robot's links is used to avoid collisions. Its magnitude is inversely proportional to the distance. Together, these forces make the goal the global minimum potential point, but local minima can stop the robot from ever reaching that point. Our approach improves on a basic, potential field paradigm developed by Munger by using an active, adaptive field - what we will call a 'flexible' potential field. Active fields are stronger when objects move towards one another and weaker when they move apart. An adaptive field's strength is individually tailored to be just strong enough to avoid any collision. In addition to the local planner, a global planning algorithm helps the planner to avoid local field minima by providing subgoals. These subgoals are based on the obstacles which caused the local planner to fail. A best-first search algorithm A* is used for graph search

Signal processing and interpretation using multilevel signal abstractions

Originally presented as author's thesis (Ph. D.--Massachusetts Institute of Technology), 1986.Bibliography: p. 216-219.Supported in part by the Advanced Research Projects Agency monitored by ONR under contract no. N00014-81-K-0742 Supported in part by the National Science Foundation under grant ECS-8407285Evangelos E. Milios