Planning Fail-Safe Trajectories for Space Robotic Arms

Abstract

A frequent concern for robot manipulators deployed in dangerous and hazardous environments for humans is the reliability of task executions in the event of a joint failure. A redundant robotic manipulator can be used to mitigate the risk and guarantee a post-failure task completion, which is critical for instance for space applications. This paper describes methods to analyze potential risks due to a joint failure, and introduces tools for fault-tolerant task design and path planning for robotic manipulators. The presented methods are based on off-line precomputed workspace models. The methods are general enough to cope with robots with any type of joint (revolute or prismatic) and any number of degrees of freedom, and might include arbitrarily shaped obstacles in the process, without resorting to simplified models. Application examples illustrate the potential of the approach.

Keywords: fail-safe trajectories; fault-tolerant manipulators; manipulation planning; robotic arms; space manipulator.

FIGURE 1

Hierarchical discretization of the end-effector pose ξ for efficient generation of the reachability map. The Cartesian space is discretized with voxels. Each voxel has an associated virtual sphere that discretizes the possible approach directions (pitch and yaw). Each surface bin in this virtual sphere has in turn an associated discretization for the roll direction.

FIGURE 2

Cross-section of the capability map for a KUKA iiwa robot, with seven DoF (joints j are marked in the figure). The HSV color scale encodes the reachability index R given by Eq. 1. Map and robot are plotted at the same scale.

FIGURE 3

Capability maps for the KUKA iiwa robot when each joint is locked at its zero position while all the other joints are fully operational. The cross-section is displayed using the same scale and the same cutting plane (XZ), but the point of view is changed in some maps to provide a better 3D visualization. Note that a failure in joint 2 or 4 significantly affects the workspace volume, while a failure in joints 6 or 7 reduces dexterity throughout the workspace (compare to the original capability map without failures in Figure 2).

FIGURE 4

Cross-section of the failure map ${\mathcal{W}}_{\mathrm{f}}$ for the KUKA iiwa robot.

FIGURE 5

Histogram of bin values of all mapped poses ξ in ${\mathcal{W}}_f$ .

FIGURE 6

Histogram of failure index F(V _i ) values in ${\mathcal{W}}_f$ .

FIGURE 7

Post-failure workspace volume of ${\mathcal{W}}_{j,l}$ as a function of l. The nominal failure-free volume is 3.292 m³.

FIGURE 8

Post-failure average dexterity in ${\mathcal{W}}_{j,l}$ as a function of l. The average dexterity for the nominal failure-free workspace is 0.578.

FIGURE 9

Normalized failure diagram for a given pose ξ; the ranges of the seven joints j have been normalized for illustration purposes (naturally, each joint has its own joint limits, which do not necessarily coincide). Yellow cells represent the current joint configuration, in this case, the upright position (all joints at zero). Green/red cells represent reachability maps ${\mathcal{W}}_{j,l}(\xi )$ that do/do not contain the pose ξ.

FIGURE 10

Failure diagrams with one highlighted joint configuration (in yellow). Each row represents one joint (similar to Figure 9). The diagrams are not normalized as in Figure 9, i.e the joint range spans from -180 to +180 deg. Regions that are out of the joint limits are represented as black cells. Top: Failure diagram showing all C-space manifold footprints. Bottom: Failure diagram showing only the C-space manifold footprint relevant for the current configuration.

FIGURE 11

Capability map spanned from the failure diagram in Figure 10 top, and cross-section of the same map. It corresponds to the post-failure return-safe workspace for all pre-image manifolds.

FIGURE 12

Capability map spanned from the failure diagram in Figure 10 bottom, and cross-section of the same map. It corresponds to the post-failure return-safe workspace only for the relevant self-motion manifold.

FIGURE 13

Online grasp selection for spacecraft docking using the plain reachability map for the manipulator. On the client satellite structure (left), green points show the kinematically feasible grasp locations, while red shows unfeasible locations for this particular relative pose between servicer and client.

FIGURE 14

Grasp selection for fail-safe spacecraft docking. The figure depicts only the bar structure used for grasping (the structure mounted on the client satellite is shown in Figure 13), and shows how the grasp possibilities change depending on the target location with respect to the servicer. The color of the structure corresponds to the v _i,p value; blue areas are preferred for grasping. The grasp pose selected must lie in a region with high v _i,p across all the maneuver sequence.

FIGURE 15

Failure-tolerant path. Left: nominal, failure-free path. Right: collection of paths to recover from random failures in each joint (as indicated by the corresponding color code).