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Soft Motion Trajectory Planner for Service Manipulator Robot
Xavier Broquère, Daniel Sidobre, Ignacio Herrera-Aguilar
TL;DR
Human-facing service robots need motion that addresses safety and comfort, motivating a soft trajectory planner with jerk, acceleration, and velocity limits. The planner computes cubic trajectories for point-to-point and path-following motion, and experiments support its validity for real-time planning and control in human presence.
Problem
Service manipulators interacting with people must address safety and comfort, with velocity limits linked to safety and acceleration and jerk bounds linked to comfort.
Source: §1 · p. 1Method
The planner computes Cartesian soft-motion trajectories using cubic curves and constrains axis durations to the longest axis for point-to-point and path-following motion.
Source: §3 · p. 2, §3.2.1 · p. 4, §3.2.2 · p. 4Results
Experiments support the approach's validity for real-time control and trajectory planning in human presence.
Source: §5 · p. 6Takeaways & Limitations
Direct computation of cubic parameters makes the planner fast enough for online use, and the authors aim to incorporate it into the path planner.
Source: §5 · p. 6Path-following duration adjustment cannot always reduce jerk, acceleration, or velocity limits; increasing jerk to shorten saturated intervals violates kinematic constraints.
Source: §3.2.2 · p. 5
Abstract
from arXiv · showhide
Human interaction introduces two main constraints: Safety and Comfort. Therefore service robot manipulator can't be controlled like industrial robotic manipulator where personnel is isolated from the robot's work envelope. In this paper, we present a soft motion trajectory planner to try to ensure that these constraints are satisfied. This planner can be used on-line to establish visual and force control loop suitable in presence of human. The cubic trajectories build by this planner are good candidates as output of a manipulation task planner. The obtained system is then homogeneous from task planning to robot control. The soft motion trajectory planner limits jerk, acceleration and velocity in cartesian space using quaternion. Experimental results carried out on a Mitsubishi PA10-6CE arm are presented.
1 INTRODUCTION
Industrial manipulators are typically used in structured spaces without human-robot interaction, while service robots must address human safety and comfort. The paper proposes bounded soft trajectories for human-facing manipulation and describes their use with path planning and online control.
1 INTRODUCTION
- Human-facing manipulators must account for safety and comfort, unlike industrial systems confined to spaces without human-robot interaction.The paper links safety to velocity limits and comfort to acceleration and jerk bounds.Source: §1 · p. 1
- Prior trajectory-planning work includes time-optimal, constraint-aware, and minimal-jerk approaches [4].Jerk-limited feed-rate optimization has also been associated with reduced contouring errors and acoustic signals.Source: §1 · p. 1
- The planner limits jerk, acceleration, and velocity in Cartesian space, including rotations, starts, and stops.The authors say these bounds support soft movement and may help integrate visual and force control loops with different time constants.Source: §1 · p. 1
- The planner computes temporal evolution along paths from HAMP and Grasp Planner, which use Move3D.The paths connect points, and the planner is used daily for this task.Source: §1 · p. 1
2 Related Work
Prior work uses polynomial profiles and transition-curve methods to produce smooth trajectories, including approaches aimed at human-robot interaction.
2 Related Work
- Related approaches range from cubic, quartic, and quintic profiles to spatial transition shaping and online seven-cubic motion.For human interaction, prior work uses seventh- or fifth-order polynomials and seven cubic equations [18].Source: §2 · pp. 1–2
3 Soft Motion Trajectory Planner
The planner generates Cartesian trajectories for an end-effector following points supplied by path-planning techniques.
3 Soft Motion Trajectory Planner
- The proposed service-robot planner limits jerk, acceleration, and velocity while planning Cartesian trajectories through path-planning points.Source: §3 · p. 2
3.1 Monodimensional Case
The monodimensional planner models motion in an acceleration–velocity frame, then derives minimal-time point-to-point motions and extends the method to nonzero initial and final kinematic conditions.
3.1.1 The elementary motions in the Acceleration-Velocity frame
- The planner’s elementary motions successively saturate jerk, acceleration, or velocity constraints, with corresponding position, velocity, acceleration, and jerk trajectories.The acceleration–velocity frame represents maximal and minimal jerk as parabolic evolutions and identifies the states at maximum and minimum velocity.Source: §3.1.1 · p. 2
3.1.2 The point to point motion
- For rest-to-rest point-to-point motion, the planner computes segment times for a minimal-time displacement using at most seven elementary motions.Optimal motions exclude simultaneous dwell at both velocity extrema and unsaturated constant-velocity segments.Source: §3.1.2 · pp. 2–3, Figure 2 · p. 3
3.1.3 Types of motions
- The two motion types are distinguished by their initial jerk segment: type 1 starts at maximum jerk, while type 2 starts at minimum jerk.For short displacements, optimal motion has no constant-velocity segment.Source: §3.1.3 · p. 3, Figure 3 · p. 4, Figure 4 · p. 4
3.1.4 The critical length
- Critical length dc separates the two motion types: distances above dc use type 1, while distances below dc use type 2.The critical motion is the minimum-time motion at the separating distance.Source: §3.1.4 · p. 3, Figure 5 · p. 4
3.1.5 The general case
- For nonzero endpoint conditions, the algorithm uses type 1/type 2 symmetry to compute segment times from endpoint conditions and jerk, acceleration, and velocity limits.Thresholds select elementary-motion lists; the most complicated cases require solving a six-degree equation representing the intersection of three parabolas.Source: §3.1.5 · pp. 3–4
3.2 Multidimensional Case
The multidimensional planner handles point-to-point motions and path-following motions through a sequence of Cartesian points. It synchronizes axis durations while respecting jerk, acceleration, and velocity constraints, with distinct adjustment challenges for transitions through intermediate points.
3.2.1 The point to point motion
- For point-to-point motion, the planner synchronizes all dimensions to the longest motion time, reducing Jmax, Amax, and Vmax in the other directions.This preserves a straight-line path while making one direction minimum-time and conditioning the others on it.Source: §3.2.1 · p. 4
3.2.2 The path following motion
- For path following, it plans adjusted point-to-point legs from P0 to P1 and P1 to Pf, then computes a transition between their motion states.At least three Cartesian points are used: the current end-effector position, the first target, and the final position.Source: §3.2.2 · p. 4
- The imposed transition time Timp is set by the axis with the largest duration after finding each axis’s optimal time.For each axis, the method first finds solution intervals between Topt and Tstop using Slowing Velocity Motion.Source: §3.2.2 · pp. 4–5
- Transition durations cannot be adjusted like point-to-point durations: lowering limits may fail at saturated endpoint velocities or when critical length exceeds D.The latter can create a time interval with no solution.Source: §3.2.2 · p. 5
- Slowing Velocity Motion can still have no solution for durations between Topt and Tstop when V0 and Vf are near Vmax; increasing jerk to shorten saturated intervals violates constraints.If Timp exceeds Tstop, the motion can instead stop and restart at P1, adding time while stopped.Source: §3.2.2 · p. 5
4 Experimental Results
The experiments use Jido, a mobile platform with a six-axis arm, to demonstrate online trajectory planning and tracking. The planner updates motion at 10 ms intervals and adjusts transition timing along a three-point path.
4.1 Experimental Platform
- Jido combines a mobile Neobotix platform with a Mitsubishi PA10 arm, and the planner runs with a 10 ms sampling time.The end-effector pose uses position and orientation coordinates; quaternion derivatives are transformed into angular velocities.Source: §4.1 · p. 5, Figure 7 · p. 5
4.2 On-line trajectory planning without time adjustment
- A 6-axis joystick supplies end-effector velocity references, while translation is planned online and angular variation is approximated using the current quaternion at 10 ms sampling.The text treats angular variation as small over each sampling interval.Source: §4.2 · p. 6
- For each direction, the distance to go is the critical length for reaching final conditions in the shortest motion; other lengths introduce oscillations.Each trajectory is replanned every 10 ms from the current state, ending at zero acceleration and the requested velocities.Source: §4.2 · p. 6
4.3 Tracking trajectory motion
- The tracking demonstration uses point-to-point motions between three translation points and adjusts transition times using intervals where Slowing Velocity Motion works.Figure 9 marks intervals without a solution as 0 and intervals with a solution as 1.Source: §4.3 · p. 6, Figure 9 · p. 6
5 Conclusions
The planner computes cubic curves directly, avoiding optimization and enabling online use. Experiments support real-time control and trajectory planning in human presence; integration into the path planner is underway.
5 Conclusions
- Directly computed cubic curves share time intervals across axes, avoid an optimization stage, and are fast enough for online use.The conclusion describes this planner as simpler than previous ones.Source: §5 · p. 6
- Experiments show the approach's validity for real-time control and trajectory planning in human presence.The authors are incorporating it into the path planner to build soft cubic curves at task-planning level and explore richer curve families.Source: §5 · p. 6