I design an instruction-driven trajectory planning system for an industrial robot inside the ADAMS environment. My purpose is to remove the separation between offline trajectory generation and continuous dynamic analysis, because many industrial robot workflows first plan a path in an external numerical tool and then import a fixed data set into ADAMS for verification. That workflow is useful, but it is not sufficiently interactive for realistic motion conditions. I therefore place the trajectory planning logic directly inside ADAMS, use the secondary development capabilities of ADAMS, and express the planned motion as reusable instructions. The resulting industrial robot model can accept target points, speeds, accelerations, and tool-frame data, generate straight-line and circular motion, solve inverse kinematics through the dynamic engine, and provide joint-level dynamic responses without leaving the simulation environment.
I treat the industrial robot as a coupled mechanical system whose end-effector trajectory is the visible task-level requirement and whose joint motion is the hidden dynamic consequence. The trajectory of the industrial robot is not only a geometric curve. It is a time-parameterized motion that must satisfy position, velocity, acceleration, and smoothness constraints. I use ADAMS as the shared platform for modeling, trajectory synthesis, inverse kinematics, and dynamic simulation. In this way, the industrial robot can be evaluated under continuous dynamic loading rather than under a small set of precomputed samples.
| Symbol | Meaning | Unit |
|---|---|---|
| \(t\) | Time variable used by the motion function | s |
| \(T\) | Total time of the current contour motion | s |
| \(t_1\) | Acceleration-stage duration | s |
| \(t_2\) | Deceleration-stage duration | s |
| \(D\) | Length of a straight-line segment | mm |
| \(\mathbf{u}\) | Unit direction vector of a straight-line segment | dimensionless |
| \(\mathbf{v}(t)\) | Velocity vector of the tool center point | mm/s |
| \(\omega\) | Angular velocity of circular motion | rad/s |
| \(\mathbf{n}\) | Normal vector of the circular plane | mm² |
| \(k(t)\) | Trajectory smoothing coefficient | dimensionless |
| \(F_x,F_y,F_z\) | Smoothed velocity functions in Cartesian directions | mm/s |
I build the system around five layers. The data layer supplies the three-dimensional geometry, kinematic parameters, dynamic parameters, and knowledge models of the industrial robot. The technology support layer provides the digital twin model, the data model, and the motion functions that allow trajectory planning inside ADAMS. The development layer contains the scripting, interface customization, and application programming interfaces that extend ADAMS. The application layer realizes trajectory planning, inverse kinematics, dynamic simulation, and performance evaluation for the industrial robot. The user layer exposes the functions through a graphical interface and displays the dynamic behavior of the industrial robot in an understandable form.
| Layer | Main role | Typical artifacts | Industrial robot relevance |
|---|---|---|---|
| Data layer | Provides geometry, kinematic, dynamic, and knowledge data | CAD models, joint limits, mass properties, tool frames | Defines the physical identity of the industrial robot |
| Technology support layer | Creates the digital twin and motion-function infrastructure | Virtual model, data model, STEP-based motion functions | Enables trajectory planning and inverse kinematics |
| Development layer | Extends ADAMS through scripts, APIs, and custom interfaces | ACL commands, Python scripts, custom dialogs | Automates industrial robot programming tasks |
| Application layer | Executes trajectory planning and dynamic analysis | MoveL, MoveC, simulation results, error metrics | Evaluates industrial robot motion quality |
| User layer | Offers interaction and visualization | Toolbars, dialogs, plots, dynamic response views | Supports industrial robot simulation and optimization |
The working principle is based on a combination of interface customization and script-based development. I create a dedicated toolbar for the industrial robot, and from that toolbar I load a trajectory planning dialog. The dialog receives target points, speed, acceleration, and tool coordinate system data. These values are passed to ADAMS design functions or runtime functions. The ADAMS solver then evaluates the motion, computes the inverse kinematics of the industrial robot, and produces joint displacements, joint velocities, joint accelerations, reaction forces, and other dynamic results. Post-processing then converts these results into plots and tables for engineering interpretation.
I use ADAMS secondary development methods in three categories. Script-based development is the most direct method because it calls built-in commands and scripts without requiring low-level code. API-based development is deeper and is used when the standard scripting interface cannot satisfy custom physical models or high-performance computation requirements. Interface customization does not extend the solver itself, but it packages scripts and API functions into user-friendly tools. For the industrial robot trajectory planning system, I combine interface customization with script-based development. This combination gives the industrial robot a practical programming front end while preserving direct access to the ADAMS dynamic engine.
| Development method | Scope | Advantages | Limitations | Use in my system |
|---|---|---|---|---|
| Script-based development | Automates ADAMS commands and model operations | Simple, fast, flexible, low implementation cost | Limited for custom solver behavior | Creates motion instructions and passes parameters |
| API-based development | Interacts with lower-level ADAMS functions | Deep customization and high-performance extension | Requires more expertise and careful maintenance | Reserved for advanced industrial robot extensions |
| Interface customization | Builds menus, toolbars, and dialogs | Improves usability and reduces operator error | Does not add solver capability by itself | Provides the industrial robot planning toolbar and dialog |
The central motion design choice is between joint motion and general motion. Joint motion applies a driver directly to a joint and lets the inverse kinematics of the mechanism determine the tool center point. General motion applies a driver directly to a marker or point in Cartesian space and then lets ADAMS compute the joint motion required to achieve that Cartesian motion. The upper-level controller of a real industrial robot usually plans in Cartesian space even though the final actuator commands are joint commands. General motion therefore matches the logical structure of industrial robot programming more closely and simplifies the expression of complex end-effector paths.
| Motion type | Control variable | Trajectory planning level | Inverse kinematics role | Fit for my industrial robot system |
|---|---|---|---|---|
| Joint motion | Joint displacement or joint velocity | Joint space | Forward kinematics gives tool pose | Useful for actuator-level studies |
| General motion | Tool center point position or velocity | Cartesian space | ADAMS solves joint motion from tool motion | Selected for instruction-based industrial robot planning |
I use the STEP function as the core smoothing primitive. STEP provides cubic Hermite interpolation, which is a classical smooth interpolation method. Its first and second derivatives are continuous within the interval, and its derivative is zero at the transition points. This satisfies the \(C^2\) continuity requirement for smooth industrial robot motion and avoids sudden acceleration changes that can cause rigid impact. When the industrial robot requires even smoother acceleration behavior, I use STEP5, which provides a higher-order transition while preserving the same instruction structure.
$$ \mathrm{STEP}(t,t_0,h_0,t_1,h_1)=h_0+(h_1-h_0)\xi^2(3-2\xi), \quad \xi=\frac{t-t_0}{t_1-t_0} $$
$$ \frac{d}{dt}\mathrm{STEP}(t,t_0,h_0,t_1,h_1)=(h_1-h_0)\frac{6\xi(1-\xi)}{t_1-t_0} $$
$$ \frac{d^2}{dt^2}\mathrm{STEP}(t,t_0,h_0,t_1,h_1)=(h_1-h_0)\frac{6(1-2\xi)}{(t_1-t_0)^2} $$
The use of STEP inside the industrial robot motion function allows each Cartesian direction to be treated as an independent smooth transition. I decompose the tool center point motion into \(X\), \(Y\), and \(Z\) components. Each component follows an accelerate-cruise-decelerate profile. I fit each component with STEP functions and then assign the fitted functions to the tool center point marker through general motion. Because the STEP function is continuously differentiable, the industrial robot receives smooth position, velocity, and acceleration commands at the interpolation level.
$$ \mathbf{p}(t)=\begin{bmatrix}x(t)\\y(t)\\z(t)\end{bmatrix} $$
$$ \mathbf{v}(t)=\frac{d\mathbf{p}(t)}{dt}=\begin{bmatrix}\dot{x}(t)\\\dot{y}(t)\\\dot{z}(t)\end{bmatrix} $$
$$ \mathbf{a}(t)=\frac{d^2\mathbf{p}(t)}{dt^2}=\begin{bmatrix}\ddot{x}(t)\\\ddot{y}(t)\\\ddot{z}(t)\end{bmatrix} $$
For a straight-line motion instruction, I define the start point \(A(x_i,y_i,z_i)\) and the target point \(B(x_j,y_j,z_j)\). The length of the straight segment is computed first. The unit direction vector from \(A\) to \(B\) then defines the spatial direction of the motion. If I multiply this unit vector by a scalar speed profile, I obtain the Cartesian velocity vector of the tool center point. This formulation is simple, explicit, and well suited to an instruction such as MoveL.
$$ D=\sqrt{(x_j-x_i)^2+(y_j-y_i)^2+(z_j-z_i)^2} $$
$$ \mathbf{u}=(u_x,u_y,u_z)=\left(\frac{x_j-x_i}{D},\frac{y_j-y_i}{D},\frac{z_j-z_i}{D}\right) $$
$$ v_x(t)=u_x v(t), \quad v_y(t)=u_y v(t), \quad v_z(t)=u_z v(t) $$
| Straight-line term | Expression | Interpretation |
|---|---|---|
| Segment length | \(D=\|\mathbf{B}-\mathbf{A}\|\) | Total distance traveled by the industrial robot tool |
| Direction vector | \(\mathbf{B}-\mathbf{A}\) | Vector from start point to target point |
| Unit vector | \(\mathbf{u}=(\mathbf{B}-\mathbf{A})/D\) | Normalized direction of the straight motion |
| Velocity vector | \(\mathbf{v}(t)=v(t)\mathbf{u}\) | Velocity of the industrial robot tool center point |
| Acceleration vector | \(\mathbf{a}(t)=\dot{v}(t)\mathbf{u}\) | Tangential acceleration along the straight path |
For a circular motion instruction, I define three points \(A(x_i,y_i,z_i)\), \(B(x_m,y_m,z_m)\), and \(C(x_j,y_j,z_j)\). The industrial robot tool center point passes through these points in sequence. The normal vector of the circular plane is obtained from the cross product of two chord vectors. The center of the circle is then computed from equal-distance conditions and the plane equation. Once the center and radius are known, I construct an orthonormal basis in the circular plane and parameterize the path by angle. This gives a clean expression for MoveC and provides the geometric foundation for smooth circular motion.
$$ \mathbf{AB}=(x_m-x_i,\;y_m-y_i,\;z_m-z_i) $$
$$ \mathbf{AC}=(x_j-x_i,\;y_j-y_i,\;z_j-z_i) $$
$$ \mathbf{n}=\mathbf{AB}\times\mathbf{AC}=(n_x,n_y,n_z) $$
$$ \hat{\mathbf{n}}=\frac{\mathbf{n}}{\|\mathbf{n}\|} $$
The circle center \(O(x_0,y_0,z_0)\) is the solution of the following linear system. The first two equations enforce equal distance from the center to the three known points. The third equation enforces that the center lies in the circular plane. This system is robust for ordinary industrial robot paths and can be solved once for each circular instruction.
$$ \begin{bmatrix}
2(x_m-x_i) & 2(y_m-y_i) & 2(z_m-z_i) \\
2(x_j-x_i) & 2(y_j-y_i) & 2(z_j-z_i) \\
n_x & n_y & n_z
\end{bmatrix}
\begin{bmatrix}
x_0 \\ y_0 \\ z_0
\end{bmatrix}
=
\begin{bmatrix}
x_m^2+y_m^2+z_m^2-(x_i^2+y_i^2+z_i^2) \\
x_j^2+y_j^2+z_j^2-(x_i^2+y_i^2+z_i^2) \\
n_x x_i+n_y y_i+n_z z_i
\end{bmatrix} $$
$$ R=\sqrt{(x_i-x_0)^2+(y_i-y_0)^2+(z_i-z_0)^2} $$
I then define an in-plane basis. The first basis vector points from the center to the start point. The third basis vector is the unit normal of the circular plane. The second basis vector is obtained by the cross product of the third and first basis vectors. With this basis, the circular path and its velocity can be written compactly. The industrial robot tool center point follows a smooth arc, and the velocity direction remains tangent to the arc.
$$ \mathbf{e}_1=\frac{\mathbf{A}-\mathbf{O}}{R}, \quad \mathbf{e}_3=\hat{\mathbf{n}}, \quad \mathbf{e}_2=\mathbf{e}_3\times\mathbf{e}_1 $$
$$ \mathbf{p}(\theta)=\mathbf{O}+R\left(\mathbf{e}_1\cos\theta+\mathbf{e}_2\sin\theta\right) $$
$$ \theta(t)=\omega t $$
$$ \mathbf{v}(t)=R\omega\left(-\mathbf{e}_1\sin(\omega t)+\mathbf{e}_2\cos(\omega t)\right) $$
The component form of circular velocity is useful because ADAMS general motion is assigned direction by direction. I therefore express \(v_x(t)\), \(v_y(t)\), and \(v_z(t)\) using the start point, the circle center, the normal vector, and the angular velocity. This produces a complete instruction-level model for circular motion of the industrial robot.
$$ v_x(t)=-\omega(x_i-x_0)\sin(\omega t)+\frac{n_y(z_i-z_0)-n_z(y_i-y_0)}{\|\mathbf{n}\|}\omega\cos(\omega t) $$
$$ v_y(t)=-\omega(y_i-y_0)\sin(\omega t)+\frac{n_z(x_i-x_0)-n_x(z_i-z_0)}{\|\mathbf{n}\|}\omega\cos(\omega t) $$
$$ v_z(t)=-\omega(z_i-z_0)\sin(\omega t)+\frac{n_x(y_i-y_0)-n_y(x_i-x_0)}{\|\mathbf{n}\|}\omega\cos(\omega t) $$
| Circular term | Expression | Purpose in industrial robot planning |
|---|---|---|
| Chord vectors | \(\mathbf{AB}\), \(\mathbf{AC}\) | Define the plane containing the circular path |
| Normal vector | \(\mathbf{n}=\mathbf{AB}\times\mathbf{AC}\) | Fix the orientation of the circular plane |
| Circle center | \(\mathbf{O}=(x_0,y_0,z_0)\) | Define the rotation center of the arc |
| Radius | \(R=\|\mathbf{A}-\mathbf{O}\|\) | Scale the circular trajectory |
| Angular velocity | \(\omega\) | Control the speed along the arc |
| Tangential velocity | \(\mathbf{v}(t)=R\omega(-\mathbf{e}_1\sin\omega t+\mathbf{e}_2\cos\omega t)\) | Provide the industrial robot velocity command |
Smoothness is not automatically guaranteed by a geometric path. Even if the path is a perfect line or a perfect circle, the industrial robot still needs a time law that avoids abrupt acceleration. I therefore define a smoothing coefficient that modulates the scalar speed. The coefficient starts at zero, rises to one during the acceleration stage, remains at one during the constant-speed stage, and falls back to zero during the deceleration stage. This coefficient is built from two STEP functions, so it inherits the continuity properties of the STEP primitive.
$$ k(t)=\mathrm{STEP}(time,0,0,t_1,1)+\mathrm{STEP}(time,T-t_2,0,T,-1) $$
I apply the smoothing coefficient to each Cartesian velocity component. The resulting functions \(F_x(t)\), \(F_y(t)\), and \(F_z(t)\) are the actual velocity inputs used by the general motion of the industrial robot. In the acceleration interval, the coefficient grows smoothly; in the cruise interval, it remains one; in the deceleration interval, it decreases smoothly. This structure is simple to parameterize and directly reflects the acceleration and deceleration behavior of a typical industrial robot controller.
$$ F_x(t)=k(t)v_x(t) $$
$$ F_y(t)=k(t)v_y(t) $$
$$ F_z(t)=k(t)v_z(t) $$
The corresponding acceleration is obtained by differentiating the product of the smoothing coefficient and the velocity component. This step is important for dynamic analysis because the industrial robot joint torques depend on acceleration as well as velocity. A smooth coefficient reduces the likelihood of discontinuous acceleration commands, and it allows the dynamic solver to produce more realistic reaction forces and joint torques.
$$ a_x(t)=\frac{d}{dt}\left[k(t)v_x(t)\right]=\dot{k}(t)v_x(t)+k(t)\dot{v}_x(t) $$
$$ a_y(t)=\frac{d}{dt}\left[k(t)v_y(t)\right]=\dot{k}(t)v_y(t)+k(t)\dot{v}_y(t) $$
$$ a_z(t)=\frac{d}{dt}\left[k(t)v_z(t)\right]=\dot{k}(t)v_z(t)+k(t)\dot{v}_z(t) $$
| Motion interval | Smoothing coefficient behavior | Industrial robot effect | |
|---|---|---|---|
| Start | \(k(t)=0\) | The industrial robot begins from rest | |
| Acceleration | \(0<k(t)<1\) | Speed increases smoothly | |
| Cruise | \(k(t)=1\) | The industrial robot follows the planned nominal speed | |
| Deceleration | \(1>k(t)>0\) | Speed decreases smoothly | |
| End | \(k(t)=0\) | The industrial robot stops without a command jump |
I implement the trajectory planning system with the secondary development functions of ADAMS. The industrial robot toolbar is the main user entry point. It contains buttons for model import, trajectory planning, simulation control, and result review. The trajectory planning dialog receives target points, speed, acceleration, tool coordinate frame, and the choice between straight-line and circular motion. The dialog then creates or modifies a general motion function. In this way, the user can plan the industrial robot motion in a manner that resembles ordinary robot programming instructions.
I use instruction names such as MoveL and MoveC to represent straight-line and circular motion. MoveL is used when the industrial robot tool center point must travel along a straight line. MoveC is used when the industrial robot tool center point must follow a circular arc through an intermediate point. For each instruction, the system computes the geometric parameters, constructs the velocity functions, applies the smoothing coefficient, and writes the general motion to the tool center point. The ADAMS solver then computes the joint motion and dynamic response of the entire industrial robot.
| Instruction | Geometry | Key inputs | Main outputs |
|---|---|---|---|
| MoveL | Straight line from start to target | Start point, target point, speed, acceleration | Cartesian velocity functions, joint trajectories |
| MoveC | Circular arc through an intermediate point | Start point, intermediate point, target point, speed, acceleration | Circular plane, center, radius, tangential velocity, joint trajectories |
I evaluate the system with a six-axis industrial robot. The simulation model is built in ADAMS, and the custom toolbar and dialog are loaded into the environment. The planned path follows a closed profile on a workpiece surface. The profile consists of straight segments and a circular segment connected in sequence. Each instruction is parameterized with the same nominal speed and acceleration. The system then generates the motion functions and performs the dynamic simulation. The resulting end-effector trajectory is compared with the theoretical path, and the joint responses are inspected for continuity and dynamic reasonableness.
| Instruction | Target point | Speed (mm/s) | Acceleration (mm/s²) | Note |
|---|---|---|---|---|
| MoveL | Target marker A | 200 | 200 | Straight-line motion |
| MoveL | Target marker B | 200 | 200 | Straight-line motion |
| MoveL | Target marker C | 200 | 200 | Straight-line motion |
| MoveL | Target marker D | 200 | 200 | Straight-line motion |
| MoveC | Intermediate marker E and target marker F | 200 | 200 | Circular motion with tangential speed and acceleration |
| MoveL | Starting marker A | 200 | 200 | Return straight-line motion |
The planned trajectory closely follows the theoretical contour. Small deviations appear near the acceleration and deceleration transitions because each segment begins and ends with a speed modulation. The straight-line cruise portions show a very small deviation, while the circular portion shows a larger deviation because the velocity direction changes continuously and the acceleration transition has a stronger influence on the industrial robot joints. This behavior is consistent with the dynamics of a multi-axis industrial robot: the circular motion requires coordinated motion of several joints, and the smoothing profile affects the joint acceleration distribution.
| Path portion | Observed deviation | Main cause | Industrial robot interpretation |
|---|---|---|---|
| Straight-line cruise | Approximately \(0.3\ \mu m\) | Discretization and solver tolerance | Highly accurate straight motion |
| Local sampled point | Approximately \(0.5\ \mu m\) | Small numerical fluctuation | Acceptable for the planned industrial robot task |
| Circular motion | Maximum approximately \(14.47\ \mu m\) | Speed, acceleration, and smoothing transitions | Circular motion is more sensitive to dynamic effects |
I also examine joint-level behavior. The angular displacement curves of all joints are smooth and continuous. This indicates that the industrial robot moves in a coordinated manner and that the inverse kinematics solution obtained through general motion is physically meaningful. The joint ranges and directions also agree with the planned task. The angular acceleration curves show that the acceleration intervals have a strong influence on dynamic smoothness. The circular segment has shorter acceleration and deceleration intervals, so its angular acceleration variation is larger. The maximum angular acceleration is about \(45^\circ/s^2\), which remains within a reasonable range for the simulated industrial robot and indicates that the motion does not contain severe impact or vibration.
| Joint | Displacement behavior | Acceleration behavior | Assessment for the industrial robot |
|---|---|---|---|
| Joint 1 | Smooth and continuous | Moderate variation | Stable base rotation |
| Joint 2 | Smooth and continuous | Moderate variation | Stable shoulder motion |
| Joint 3 | Smooth and continuous | Moderate variation | Stable elbow motion |
| Joint 4 | Smooth and continuous | Higher variation near circular segment | Acceptable wrist response |
| Joint 5 | Smooth and continuous | Higher variation near circular segment | Acceptable wrist response |
| Joint 6 | Smooth and continuous | Moderate variation | Stable tool orientation |
The inverse kinematics behavior is one of the main advantages of the proposed industrial robot system. Because the general motion is defined at the tool center point, ADAMS solves the joint motion required to achieve that Cartesian trajectory. I do not need to manually derive closed-form inverse kinematics for every instruction. The dynamic solver handles the constraint equations and produces joint trajectories that satisfy the mechanism. This makes the system convenient for industrial robot simulation, especially when the trajectory planner, controller, and mechanical model are studied together.
$$ \mathbf{q}(t)=\mathrm{IK}\left(\mathbf{p}_d(t),\mathbf{R}_d(t),\mathbf{c}\right) $$
In the equation above, \(\mathbf{q}(t)\) is the joint vector of the industrial robot, \(\mathbf{p}_d(t)\) is the desired tool center point position, \(\mathbf{R}_d(t)\) is the desired tool orientation, and \(\mathbf{c}\) represents configuration choices such as elbow-up or wrist-flip. The ADAMS general motion provides \(\mathbf{p}_d(t)\) directly, and the constraint solver determines \(\mathbf{q}(t)\). This is a practical way to connect instruction-level trajectory planning with dynamic simulation of the industrial robot.
The trajectory smoothing coefficient plays a central role in the quality of the industrial robot motion. If the coefficient changes too quickly, the acceleration command becomes large and the joint torques may fluctuate. If the coefficient changes too slowly, the motion takes longer and may reduce productivity. I can tune the acceleration duration \(t_1\) and deceleration duration \(t_2\) independently. This gives a simple but effective method for balancing motion quality and cycle time. The same framework can be extended to higher-order smoothing by replacing STEP with STEP5, which further reduces jerk and improves the dynamic behavior of the industrial robot.
| Design parameter | Effect on industrial robot motion | Practical consideration |
|---|---|---|
| \(t_1\) | Controls acceleration smoothness | Longer duration reduces acceleration peaks |
| \(t_2\) | Controls deceleration smoothness | Longer duration reduces stopping impact |
| Nominal speed | Sets cruise velocity | Higher speed reduces cycle time but increases dynamic load |
| Nominal acceleration | Sets acceleration scale | Must respect joint torque and actuator limits |
| STEP order | Controls continuity order | STEP5 improves jerk behavior for sensitive tasks |
I consider the dynamic consequences of the planned trajectory for the industrial robot. The joint torque depends on inertial forces, Coriolis and centrifugal effects, gravity, and external loading. When the trajectory is planned directly inside ADAMS, the relationship between the Cartesian instruction and the joint torque is available without data exchange between separate tools. This is valuable for industrial robot design because the engineer can observe how a change in target point, speed, or acceleration affects the load on each joint. It is also valuable for control tuning because the same model can be used to test feedforward and feedback strategies.
$$ \boldsymbol{\tau}=\mathbf{M}(\mathbf{q})\ddot{\mathbf{q}}+\mathbf{C}(\mathbf{q},\dot{\mathbf{q}})\dot{\mathbf{q}}+\mathbf{g}(\mathbf{q})+\mathbf{J}^T\mathbf{F}_{ext} $$
In this dynamic equation, \(\boldsymbol{\tau}\) is the joint torque vector, \(\mathbf{M}(\mathbf{q})\) is the inertia matrix, \(\mathbf{C}(\mathbf{q},\dot{\mathbf{q}})\) contains Coriolis and centrifugal terms, \(\mathbf{g}(\mathbf{q})\) is the gravity vector, \(\mathbf{J}\) is the Jacobian, and \(\mathbf{F}_{ext}\) is the external force at the tool. The planned trajectory influences every term through \(\mathbf{q}(t)\), \(\dot{\mathbf{q}}(t)\), and \(\ddot{\mathbf{q}}(t)\). By generating the trajectory in ADAMS, I can evaluate these terms continuously during the motion of the industrial robot.
| Dynamic quantity | Dependence on trajectory | Use for industrial robot evaluation |
|---|---|---|
| Joint displacement | Inverse kinematics from Cartesian path | Workspace and configuration check |
| Joint velocity | First derivative of joint displacement | Speed limit and actuator check |
| Joint acceleration | Second derivative of joint displacement | Smoothness and impact assessment |
| Joint torque | Full dynamic equation | Load capacity and drive sizing |
| Reaction force | Constraint and inertial loads | Structural and foundation evaluation |
I compare the proposed instruction-based method with a conventional offline workflow. In the conventional workflow, the industrial robot trajectory is planned in an external numerical environment, sampled at discrete times, and then imported into ADAMS as a fixed data set. The dynamic analysis is performed after the trajectory is frozen. If the engineer wants to change a target point or speed, the entire workflow must be repeated. In my method, the trajectory remains parametric inside ADAMS. The industrial robot instruction can be edited, regenerated, and simulated again without rebuilding the external data pipeline. This improves real-time interaction and supports continuous dynamic analysis.
| Aspect | Conventional offline workflow | My ADAMS instruction-based workflow |
|---|---|---|
| Trajectory source | External planner or sampled data | ADAMS motion instructions |
| Interactivity | Limited after data import | High through dialogs and scripts |
| Dynamic analysis | Performed after trajectory freeze | Continuous during simulation |
| Parameter change | Requires external replanning | Direct edit and rerun |
| Inverse kinematics | Often solved externally | Solved by ADAMS constraint engine |
| Industrial robot programming style | Data-oriented | Instruction-oriented |
I also note several practical implementation details. The tool center point must be defined consistently with the industrial robot tool frame. Target markers must be associated with the correct reference frame. The acceleration and deceleration times should be chosen with respect to the total segment time. If \(t_1+t_2\) exceeds the total motion time, the cruise interval disappears and the smoothing function becomes a direct transition from acceleration to deceleration. This can be acceptable for short segments, but it changes the dynamic response. I therefore check the time parameters before generating the motion instruction.
| Implementation condition | Required check | Consequence for the industrial robot |
|---|---|---|
| Tool frame definition | Marker and tool center point alignment | Correct end-effector motion |
| Target marker validity | Target point within reachable workspace | Feasible inverse kinematics |
| Time parameter consistency | \(t_1+t_2\le T\) | Existence of a cruise interval |
| Velocity and acceleration limits | Compare with joint limits | Feasible industrial robot operation |
| Contour continuity | Position and tangent continuity at segment joins | Smooth transition between instructions |
The contour used in my evaluation contains multiple straight segments and one circular segment. The circular segment is the most demanding because it requires continuous change of the velocity direction. The smoothing coefficient modulates the speed magnitude, but the direction change remains governed by the circular geometry. The combination of speed smoothing and geometric continuity determines the final joint acceleration. The measured maximum deviation in the circular portion is larger than in the straight portions, but it remains small relative to the scale of the industrial robot task. This supports the conclusion that the instruction-based trajectory planning method is effective.
I further examine how the smoothing coefficient affects the transition between consecutive instructions. At the end of one instruction and the beginning of the next, the position must match, and the velocity should be continuous if the industrial robot is not intended to stop. In my current implementation, each instruction includes its own acceleration and deceleration stages, so the industrial robot can stop smoothly at the end of each segment. For continuous contour following, the smoothing parameters can be arranged so that the deceleration of one segment and the acceleration of the next segment overlap or blend. This is an important extension for high-speed industrial robot applications.
$$ \mathbf{p}_{end}^{(i)}=\mathbf{p}_{start}^{(i+1)} $$
$$ \mathbf{v}_{end}^{(i)}=\mathbf{v}_{start}^{(i+1)} $$
When the velocity continuity condition is satisfied, the industrial robot does not hesitate at the instruction boundary. The dynamic response remains smooth, and the controller does not need to command a sudden stop. When the velocity continuity condition is not satisfied, the industrial robot may experience a short acceleration spike. My system allows the engineer to inspect this behavior directly in ADAMS and adjust the smoothing parameters before the trajectory is deployed to a real industrial robot.
| Boundary condition | Mathematical condition | Motion quality implication |
|---|---|---|
| Position continuity | \(\mathbf{p}_{end}^{(i)}=\mathbf{p}_{start}^{(i+1)}\) | Avoids geometric jump |
| Velocity continuity | \(\mathbf{v}_{end}^{(i)}=\mathbf{v}_{start}^{(i+1)}\) | Avoids speed discontinuity |
| Acceleration continuity | \(\mathbf{a}_{end}^{(i)}=\mathbf{a}_{start}^{(i+1)}\) | Reduces impact and vibration |
| Jerk limitation | Higher-order STEP or blending | Improves delicate industrial robot tasks |
The system also provides a foundation for digital twin development of the industrial robot. A digital twin needs more than a geometric model. It needs a live connection between commands, states, and dynamic responses. My instruction-based trajectory planner supplies this connection inside ADAMS. The command is expressed as an industrial robot instruction, the state is computed by the solver, and the response is visualized through joint curves, tool paths, and dynamic quantities. This structure can be extended to include controller models, sensor models, and external process models.
| Digital twin element | Implementation in my system | Benefit for industrial robot engineering |
|---|---|---|
| Virtual geometry | ADAMS model of the six-axis industrial robot | Accurate spatial and inertial representation |
| Motion command | MoveL and MoveC instructions | Readable and reusable trajectory definition |
| State computation | ADAMS solver and constraint equations | Continuous dynamic state of the industrial robot |
| Performance visualization | Joint displacement, acceleration, path error | Fast engineering diagnosis |
| Optimization loop | Parameter editing and resimulation | Iterative improvement of industrial robot motion |
I observe that the proposed method is especially useful when the industrial robot must perform many similar tasks with small variations. For example, a production cell may require the same contour to be followed with different tool offsets, speeds, or target positions. In a conventional workflow, each variation may require a new external trajectory file. In my workflow, each variation is a parameter change in the instruction dialog. The industrial robot model remains the same, and the dynamic analysis is repeated immediately. This reduces engineering effort and improves consistency.
The method also supports dynamic optimization of the industrial robot. The engineer can define an objective such as minimizing cycle time, reducing joint torque peaks, or limiting tool deviation. The parameters available for optimization include target points, nominal speed, nominal acceleration, acceleration duration, deceleration duration, and STEP order. Because the trajectory is generated inside ADAMS, the optimization loop can call the same simulation model repeatedly. This creates a closed loop of trajectory generation, dynamic verification, and control-oriented improvement.
$$ \min_{\mathbf{x}} \; J(\mathbf{x}) = w_1 T_{cycle}(\mathbf{x})+w_2 \max_t \|\boldsymbol{\tau}(t,\mathbf{x})\|+w_3 \max_t \|\mathbf{e}(t,\mathbf{x})\| $$
In this objective function, \(\mathbf{x}\) is the vector of trajectory parameters, \(T_{cycle}\) is the cycle time, \(\boldsymbol{\tau}\) is the joint torque, \(\mathbf{e}\) is the path error, and \(w_1\), \(w_2\), and \(w_3\) are weighting factors. The constraints can include joint position limits, joint velocity limits, joint acceleration limits, and actuator torque limits. This formulation gives a direct connection between the instruction parameters and the physical performance of the industrial robot.
| Optimization variable | Physical meaning | Typical constraint |
|---|---|---|
| Target point | Task geometry | Reachable workspace of the industrial robot |
| Nominal speed | Cruise velocity | Joint velocity limit |
| Nominal acceleration | Acceleration scale | Joint torque limit |
| \(t_1,t_2\) | Smoothing durations | Cycle time and acceleration limit |
| STEP order | Continuity level | Controller and computation capability |
I conclude that the instruction-based trajectory planning system provides a practical bridge between industrial robot programming and ADAMS dynamic simulation. The system uses a five-layer architecture, combines interface customization with script-based development, and represents motion through MoveL and MoveC instructions. Straight-line motion is described by a unit direction vector and a scalar speed profile. Circular motion is described by three points, a plane normal, a circle center, a radius, and a tangential velocity function. The smoothing coefficient based on STEP functions ensures continuous and smooth motion. The ADAMS general motion then solves the inverse kinematics of the industrial robot and produces continuous joint trajectories.
The simulation results show that the planned trajectory follows the theoretical path with small deviations. The straight-line cruise portions have deviations on the order of a few tenths of a micrometer, and the circular portion has a maximum deviation of about \(14.47\ \mu m\). The joint displacement curves are smooth and continuous, and the joint acceleration remains within a reasonable range, with a maximum of about \(45^\circ/s^2\). These results indicate that the proposed method satisfies the motion requirements of the industrial robot and provides a new approach for industrial robot simulation and optimization.
I see several directions for further development. One direction is to add blending between consecutive instructions so that the industrial robot can follow long contours without stopping at every segment boundary. Another direction is to include a controller model in the loop so that servo dynamics, tracking errors, and communication delays can be evaluated. A third direction is to extend the instruction set to include joint-space motion, tool orientation interpolation, force-controlled motion, and process-specific instructions such as welding or painting. A fourth direction is to connect the ADAMS model with real industrial robot data for online calibration and digital twin updating.
| Future extension | Expected benefit | Industrial robot application |
|---|---|---|
| Instruction blending | Continuous contour motion without stops | High-speed path following |
| Controller model | More realistic servo and tracking behavior | Control tuning and validation |
| Orientation interpolation | Full pose planning | Welding, painting, assembly |
| Force control | Interaction with environment | Polishing, grinding, assembly |
| Online data connection | Digital twin updating | Predictive maintenance and monitoring |
From my perspective, the most important outcome is that the industrial robot trajectory is no longer a static input to a dynamic model. It becomes a programmable object inside the simulation environment. The engineer can change the instruction, observe the dynamic response, and optimize the motion without leaving ADAMS. This makes the trajectory planning system useful not only for analysis but also for design. It supports the study of joint loads, actuator sizing, structural vibration, cycle time, and path accuracy in a unified workflow.
I therefore present the ADAMS-based instruction-driven trajectory planning system as a complete method for industrial robot motion generation and dynamic evaluation. The method is modular, parameterized, and extensible. It uses standard ADAMS capabilities, avoids unnecessary external data exchange, and preserves the programming style of an industrial robot controller. The combination of MoveL and MoveC instructions, STEP-based smoothing, general motion, and ADAMS inverse kinematics provides a coherent foundation for high-quality industrial robot simulation. The results confirm that the trajectory meets the motion requirements, and the approach offers a useful new path for industrial robot simulation, control development, and optimization.