For the grasping pose selection, several papers investigate manipulability and dex- terity [134, 145, 52] to evaluate the grasp configuration. However, they focus only on the evaluation of arm configuration without considering collisions during arm mo- tion planning. Several algorithms have attempted to enhance grasping selection by using an integrative method for grasping and planning [77,50,122], but they require pre-learned information for the tasks.
In general, redundant manipulators with more than six degrees of freedom (DoF) have no analytic solution to the Inverse Kinematics (IK) problem. There are several sampling-based planning approaches for grasping and motion planning without ex- plicit IK solutions or specific goal configurations [137, 132, 28, 16, 133]. Ciocarlie et al. [28] suggest collision-aware inverse kinematics for grasp selection by searching a feasible grasp configuration corresponding to the desired end-effector pose over the pa- rameterized redundant joints. While their method finds a feasible solution efficiently, it is unable to choose an optimal solution for grasp planning. In order to perform sampling-based planning approaches without a specific grasp configuration, Weghe et al. use the Jacobian Transpose (JT) between the target pose and the current pose [137], and Bertram et al. [16] suggest the IK-RRT, which generates random target configurations from plausible grasp configurations in order to exploit the advantages of the bi-directional RRT [132, 133]. However, these approaches have the limitation that they are unable to impose orientation constraints.
Regarding sampling-based planning for transport with constraints, Berenson et al. [13] suggest the projection of random configurations to the region defined by the manifold of constraints (CBiRRT). Many approaches suggest different iterative projection methods based on a similar framework [124,140,100, 79]. However, these
approaches have the disadvantage that infeasible samples are projected on the bound- ary as opposed to the center of the nearest constraint manifold. In another approach, Stilman [124] suggests tangent-space (TS) and first-order retraction (FR) sampling schemes that are able to explore the entire C-space of constrained motion. However, their method still considers only hard constraints, and it could be inefficient in the cluttered environment since it finds the optimal solution iteratively and then checks for collisions at the end.
There are several methods for sampling-based motion planning with constraints [73] for real applications. Atlas-based RRT [65] projects a random point to a tangent space of the chart of the manifold. To improve the tree extension within the constraint manifold, it keeps the extension in the chart until it reaches the random point or the new node is unable to satisfy the constraint. However, Atlas-based RRT is time consuming for finding the neighboring charts when adding a chart to the atlas, and the mapping onto the atlas requires heavy computation. Tangent bundle RRT [71] projects the new node onto the constraint manifold and generates a new tangent space only when the RRT tree reaches a boundary of the constraint manifold or when the distance from the new node is larger than a certain threshold. This approach can significantly reduce the number of projections to the manifold. Kang and Park [68] suggest a Gaussian Process approach for a point-to-manifold distance function based on GMMs of a given data set in the constrained manifold. Since the representation is differentiated and it can obtain the gradient of the point-to-manifold distance function analytically, it applies CBiRRT without an iterative projection process for several constrained planning problems. While these approaches handle hard constraint, such as a closed chain constraint problem, our approach focuses on soft-constraints. We define cost functions including constraints and find a sample to minimize this cost function. This framework is appropriate for problems with soft constraints, such as maintaining the end-effector pose.
Whereas most constrained sampling-based planning approaches consider only hard constraints, Kunz and Stilman [79] handle soft constraints, such as the pose of the grasped object. The overall procedure is similar to that of CBiRRT [14] except for
the distance metric of joint space error. It also uses an iterative Jacobian pseudo- inverse to find the configuration that satisfies the constraints. Although they consider soft constraints, there is still the limitation of slowdown in the cluttered environment since the iterative Jacobian pseudo-inverse is applied for convergence to constraint manifolds.
Regarding sampling in the task space, Shkolnik et al. [119] suggest using a sam- pling approach directly in the task space considering collisions. The Jacobian pseudo- inverse method is used for the growth of the tree. It is able to reduce the computa- tional time dramatically since sampling and searches for nearest neighbors in the task space are able to reduce the dimensionality and guide the RRT growth efficiently to the goal. However, in order to perform the RRT in the task space, there should be an efficient method for finding a configuration corresponding to a node in the task space. The suggested Jacobian pseudo-inverse method is effective if the task space is an open space with few obstacles, but it is difficult to use when the environment is cluttered with obstacles as explained in [135]. Furthermore, this approach considers only the position state in the task space, and it is limited, being unable to consider soft constraints.
The key feature of our approach in this thesis is that we exploit theplanning mar- gin and the parameterized intermediate configuration for grasping with constraints. Our approach also proposes sampling-based planning of transport manipulation tasks that incorporates soft constraints via appropriate cost penalties.