This paper, based on the idea of redundancy angle discretisation, proposes an obstacle avoidance method for the fixed tip pose trajectory of a seven degrees-of-freedom (7-DOF) modular manipulator. First, for the case in which a specific redundancy angle is given, the analytical solutions of the redundant manipulator left 6-DOF subchain are found. Then, through the discretisation of the redundancy angle, the concept of the self-motion space of the tip pose is proposed and is extended to the concept of the self-motion space of the trajectory. Based on this discrete space, a path-planning algorithm is proposed to help select the appropriate redundancy angles to obtain the collision-free solution set of the fixed Cartesian trajectory. However, due to the large fluctuation of the obtained path, a path optimisation method based on the path cost is proposed to smooth the path, and the continuous and collision-free solution set of the manipulator tip’s trajectory is obtained. The method proposed in this paper provides a new thought for the problem of collision-free solution set planning for the Cartesian trajectory of a 7-DOF manipulator and it has great application potential in working environments with high accuracy requirements for the trajectory.

For a grasping task planner, the pre-planning of the reachable tip pose in a manipulator’s workspace is important. On this basis, for a seven-degree-of-freedom (7-DOF) redundant manipulator, it is very meaningful to study how to give full play to its redundant characteristics to achieve more dexterous grasping. In this paper, through the improved shape primitive method, the reachability spheres of the 7-DOF manipulator studied were more accurately captured, and a more accurate reachability capability map was generated. Then, based on the idea of redundancy angle discretization, the concept of the obstacle avoidance ability (OAA) index is innovatively proposed to measure the dexterity of the grasping task of the manipulator in a certain tip pose. Based on the OAA index axis, the distribution of the OAA index in each reachability sphere was analyzed. The prediction models of the OAA index of all reachability spheres in the workspace of the manipulator were obtained by the Levenberg–Marquardt algorithm and finally formed a dexterity capability map of the manipulator, which provides a new idea for the pre-planning of the dexterous grasping task of the redundant manipulator. Finally, we give the general frameworks of different grasping pre-planning by combining two kinds of capability maps and verify the effect.