Faster Motion on Cartesian Paths Exploiting Robot Redundancy at the Acceleration Level

The problem of minimizing the transfer time along a given Cartesian path for redundant robots can be approached in two steps, by separating the generation of a joint path associated to the Cartesian path from the exact minimization of motion time under kinematic/dynamic bounds along the obtained parameterized joint path. In this framework, multiple suboptimal solutions can be found, depending on how redundancy is locally resolved in the joint space within the first step. We propose a solution method that works at the acceleration level, by using weighted pseudoinversion, optimizing an inertia-related criterion, and including null-space damping. Several numerical results obtained on different robot systems demonstrate consistently good behaviors and definitely faster motion times in comparison with related methods proposed in the literature. The motion time obtained with our method is reasonably close to the global time-optimal solution along same Cartesian path. Experimental results on a KUKA LWR IV are also reported, showing the tracking control performance on the executed motions

Passive Compliance Control of Redundant Serial Manipulators

Current industrial robotic manipulators, and even state of the art robotic manipulators, are slower and less reliable than humans at executing constrained manipulation tasks, tasks where motion is constrained in some direction (e.g., opening a door, turning a crank, polishing a surface, or assembling parts). Many constrained manipulation tasks are still performed by people because robots do not have the manipulation ability to reliably interact with a stiff environment, for which even small commanded position error yields very high contact forces in the constrained directions. Contact forces can be regulated using compliance control, in which the multi-directional elastic behavior (force-displacement relationship) of the end-effector is controlled along with its position. Some state of the art manipulators can directly control the end-effector\u27s elastic behavior using kinematic redundancy (when the robot has more than the necessary number of joints to realize a desired end-effector position) and using variable stiffness actuators (actuators that adjust the physical joint stiffness in real time). Although redundant manipulators with variable stiffness actuators are capable of tracking a time-varying elastic behavior and position of the end-effector, no prior work addresses how to control the robot actuators to do so. This work frames this passive compliance control problem as a redundant inverse kinematics path planning problem extended to include compliance. The problem is to find a joint manipulation path (a continuous sequence of joint positions and joint compliances) to realize a task manipulation path (a continuous sequence of end-effector positions and compliances). This work resolves the joint manipulation path at two levels of quality: 1) instantaneously optimal and 2) globally optimal. An instantaneously optimal path is generated by integrating the optimal joint velocity (according to an instantaneous cost function) that yields the desired task velocity. A globally optimal path is obtained by deforming an instantaneously generated path into one that minimizes a global cost function (integral of the instantaneous cost function). This work shows the existence of multiple local minima of the global cost function and provides an algorithm for finding the global minimum

Point trajectory planning of flexible redundant robot manipulators using genetic algorithms

The paper focuses on the problem of point-to-point trajectory planning for flexible redundant robot manipulators (FRM) in joint space. Compared with irredundant flexible manipulators, a FRM possesses additional possibilities during point-to-point trajectory planning due to its kinematics redundancy. A trajectory planning method to minimize vibration and/or executing time of a point-to-point motion is presented for FRMs based on Genetic Algorithms (GAs). Kinematics redundancy is integrated into the presented method as planning variables. Quadrinomial and quintic polynomial are used to describe the segments that connect the initial, intermediate, and final points in joint space. The trajectory planning of FRM is formulated as a problem of optimization with constraints. A planar FRM with three flexible links is used in simulation. Case studies show that the method is applicable

Kinematically optimal hyper-redundant manipulator configurations

“Hyper-redundant” robots have a very large or infinite degree of kinematic redundancy. This paper develops new methods for determining “optimal” hyper-redundant manipulator configurations based on a continuum formulation of kinematics. This formulation uses a backbone curve model to capture the robot's essential macroscopic geometric features. The calculus of variations is used to develop differential equations, whose solution is the optimal backbone curve shape. We show that this approach is computationally efficient on a single processor, and generates solutions in O(1) time for an N degree-of-freedom manipulator when implemented in parallel on O(N) processors. For this reason, it is better suited to hyper-redundant robots than other redundancy resolution methods. Furthermore, this approach is useful for many hyper-redundant mechanical morphologies which are not handled by known methods

Stable Torque Optimization for Redundant Robots Using a Short Preview

We consider the known phenomenon of torque oscillations and motion instabilities that occur in redundant robots during the execution of sufficiently long Cartesian trajectories when the joint torque is instantaneously minimized. In the framework of online local redundancy resolution methods, we propose basic variations of the minimum torque scheme to address this issue. Either the joint torque norm is minimized over two successive discrete-time samples using a short preview window, or we minimize the norm of the difference with respect to a desired momentum-damping joint torque, or the two schemes are combined together. The resulting local control methods are all formulated as well-posed linear quadratic problems, and their closed-form solutions also generate low joint velocities while addressing the primary torque optimization objectives. Stable and consistent behaviors are obtained along short or long Cartesian position trajectories, as illustrated with simulations on a 3R planar arm and with experiments on a 7R KUKA LWR robot

Optimal redundancy control for robot manipulators

Optimal control for kinematically redundant robots is addressed for two different optimization problems. In the first optimization problem, we consider the minimization of the transfer time along a given Cartesian path for a redundant robot. This problem can be solved in two steps, by separating the generation of a joint path associated to the Cartesian path from the exact minimization of motion time under kinematic/dynamic bounds along the obtained parametrized joint path. In this thesis, multiple sub-optimal solutions can be found, depending on how redundancy is locally resolved in the joint space within the first step. A solution method that works at the acceleration level is proposed, by using weighted pseudoinversion, optimizing an inertia-related criterion, and including null-space damping. The obtained results demonstrate consistently good behaviors and definitely faster motion times in comparison with related methods proposed in the literature. The motion time obtained with the proposed method is close to the global time-optimal solution along the same Cartesian path. Furthermore, a reasonable tracking control performance is obtained on the experimental executed motions. In the second optimization problem, we consider the known phenomenon of torque oscillations and motion instabilities that occur in redundant robots during the execution of sufficiently long Cartesian trajectories when the joint torque is instantaneously minimized. In the framework of on-line local redundancy resolution methods, we propose basic variations of the minimum torque scheme to address this issue. Either the joint torque norm is minimized over two successive discrete-time samples using a short preview window, or we minimize the norm of the difference with respect to a desired momentum-damping joint torque, or the two schemes are combined together. The resulting local control methods are all formulated as well-posed linear-quadratic problems, and their closed-form solutions generate also low joint velocities while addressing the primary torque optimization objectives. Stable and consistent behaviors are obtained along short or long Cartesian position trajectories. For the two addressed optimization problems in this thesis, the results are obtained using three different robot systems, namely a 3R planar arm, a 6R Universal Robots UR10, and a 7R KUKA LWR robot

Cartesian control of redundant robots

A Cartesian-space position/force controller is presented for redundant robots. The proposed control structure partitions the control problem into a nonredundant position/force trajectory tracking problem and a redundant mapping problem between Cartesian control input F is a set member of the set R(sup m) and robot actuator torque T is a set member of the set R(sup n) (for redundant robots, m is less than n). The underdetermined nature of the F yields T map is exploited so that the robot redundancy is utilized to improve the dynamic response of the robot. This dynamically optimal F yields T map is implemented locally (in time) so that it is computationally efficient for on-line control; however, it is shown that the map possesses globally optimal characteristics. Additionally, it is demonstrated that the dynamically optimal F yields T map can be modified so that the robot redundancy is used to simultaneously improve the dynamic response and realize any specified kinematic performance objective (e.g., manipulability maximization or obstacle avoidance). Computer simulation results are given for a four degree of freedom planar redundant robot under Cartesian control, and demonstrate that position/force trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed controller