dai2022review

A Review of Spatial Robotic Arm Trajectory Planning

Authors: Dai, Xiang, Zhang, Jiang, Qu, Zhang · Year: 2022 · Venue: Aerospace (MDPI), 9(7), 361
Raw: md

Summary

A survey of trajectory-planning methods for space robotic arms, organized into two branches: (1) obstacle-avoidance planning driven by collision-avoidance requirements, and (2) motion-trajectory planning driven by smoothness/optimality requirements. It catalogs collision-detection primitives (bounding volumes), classical obstacle-avoidance planners (pseudo-inverse, APF, C-space, A*, RRT), interpolation-based joint-space planners (polynomials, B-splines, NURBS, Bézier), and intelligent optimizers (GA, PSO, reinforcement learning). The paper is a literature map, not a new derivation; its value to us is as an index into the FFSM planning literature and a statement of the field’s open problems.

Key Claims

• The defining feature of a space arm vs a ground arm is the floating base: in free-floating mode the base is uncontrolled, linear and angular momentum are conserved, and this conservation acts as a nonholonomic constraint producing kinematic and dynamic coupling between arm and base (Sec. 2).
• Dynamic singularities of a free-floating robot differ from the kinematic singularities of a fixed-base arm; they arise from the dynamic-body Jacobian rather than the kinematic Jacobian (citing Rybus et al., ref. [81]).
• Joint-space planning has “no redundancy and singularities” but incurs end-effector trajectory error; Cartesian-space planning is intuitive/accurate but inversion-heavy and exposes singularities (Table 2).
• Pseudo-inverse planners express solutions as least-norm particular solution plus null-space term; their limitations are difficulty enforcing joint constraints and the cost of repeated pseudo-inversion.
• Lu et al. (ref. [46]) cast FFSM trajectory planning with end-effector tracking and joint angle/velocity/acceleration limits as a constrained convex QP, and use it to avoid the dynamic singularity of the FFSM.
• Wang et al. (ref. [79]) plan optimal joint trajectories for a free-floating robot using the reaction null-space, parameterizing joint motion by Bézier curves whose control points are optimized by constrained differential evolution.
• No single intelligent algorithm yet simultaneously delivers global convergence, real-time solving, accuracy, generality, and simplicity (stated open problem, Sec. 4).

Method

This is a review; it transcribes few equations. The regime treated throughout is explicitly free-FLOATING (uncontrolled base, momentum-conserving, nonholonomic), which is the dual of our free-FLYING assumption (fully-actuated 6-DOF base). The coupling and dynamic-singularity phenomena the paper foregrounds are precisely the artifacts the free-flying actuated base is meant to remove, so the paper is useful mainly as a contrast case and as a planner taxonomy.

Transcribed relations (paper notation):

• Pseudo-inverse with null-space projection: joint rates from J^+ (pseudo-inverse of Jacobian J) plus the null-space projector (I - J^+ J) for obstacle avoidance / self-motion.

• C-space obstacle (Eq. unnumbered, p. 8):
  $C{O}_{robot}(B)=\{x\in Cspac{e}_{robot}\mid (robot{)}_x\cap B\ne 0\}$
  where (robot)_x is the robot’s occupancy at joint configuration x; x ∈ CO_robot(B) means interference with obstacle B.

• PSO update (p. 13):
  $v_{id}^{k+1}=w{v}_{id}^k+c_1{r}_1(p_{id}-x_{id}^k)+c_2{r}_2(p_{gd}-x_{id}^k)$
  $x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1}$
  with inertia weight w, cognitive/social weights c_1, c_2, random r_1, r_2 ∈ [0,1], personal best p_{id}, global best p_{gd}.

Note: the markdown renders the C-space set-builder with ≠ 0 rather than ≠ ∅; this is the source’s own notation (likely an OCR/typesetting artifact for the empty set), flagged here.

Relevance to thesis

The paper is the field’s planning taxonomy and a curated bibliography for FFSM guidance/planning — useful for situating our free-flying work and for sourcing baseline planners. Critically, it articulates the free-floating pathologies (momentum-conservation nonholonomy, dynamic coupling, dynamic singularities distinct from kinematic ones, base attitude perturbation) that motivate a fully-actuated base. Several cited results (reaction null-space joint planning, convex-QP dynamic-singularity avoidance, RRT/Bézier singularity-aware trajectories) are candidate baselines or contrasts for our nominal algorithms before the risk layer.

Connections

Topics: motion_planning · free_flying_vs_free_floating · dynamic_singularity · reaction_null_space · generalized_jacobian

Key Equations / Quotes

“The most significant difference between the space robotic arm and the ground robotic arm is that the base is floating. Since the base of the space arm is not fixed, the base position is not controlled in the free-floating mode of operation, so the linear momentum and angular momentum of the whole robotic arm system are conserved. There is a non-integrity limitation in the robotic arm system, resulting in kinematic and dynamical coupling between the robotic arm and the base during the motion” (p. 3)

“Jacobian was used to find dynamically singular configurations (these configurations differ from the kinematically singular configurations obtained for a fixed-base manipulator).” (p. 11)

“no redundancy and singularities … However, there are errors in the end trajectories” — joint-space planning characteristics (Table 2, p. 9)

Open Questions

• No algorithm yet meets global convergence, real-time solving, accuracy, generality, and simplicity together — which trade-offs are acceptable for an actuated free-flying base?
• Optimal selection of interpolation-curve order/type per task remains unresolved; higher order raises solve cost without clear benefit.
• Multi-objective on-orbit planning under realistic operating conditions (life, vibration, energy, speed simultaneously) is largely unaddressed.
• The survey treats only free-floating dynamics; it does not characterize how the taxonomy changes when the base is fully actuated (our regime).